The training sequence in G in episode 9 shows the differences in the physical capabilities of the Gear Wielders. Tsubasa is the one having the least trouble with the training, showing how she's been doing this since young and thus is the most physically fit. Hibiki shows signs of struggling at times, but is able to keep up, fitting with her close combat style. But Chris is wiped out early on. This isn't just for laughs; Chris is a long range combatant. She's not that good when it comes to close range combat and thus this training style doesn't really suit her.
The two duets the Queens of Music give us reflect their relationships in the respective seasons. "Fushichou no Flamme" from G was a tumultuous, aggressive song, underscoring the competition between Tsubasa and Maria first as rival idols, then as leaders of their respective Symphogear teams. In contrast, "Seiten Galaxy Cross" from GX is a more typical ballad song, sung in harmony, outlining the progress made since G, and the improved relationship between Tsubasa and Maria as a result.
The two duets provided by Shirabe and Kirika also reflect the relationship between the two to an extent in regards to when the duet shows up in their respective seasons. "Edge Works of Goddess ZABABA" from G is very aggressive and fits the tone of Episodes 11 and 12 where Shirabe and Kirika have to fight against each other. "Just Loving X-Edge" of GX, in contrast, has more of a light-hearted feel which fits the heroic mood of Episode 5 where Shirabe and Kirika fight together to Hold the Line for their friends.
It's stated that Elfnein was a homunculus crafted by Carol and given her memories. The reason for this becomes obvious in GX E6, when Elfnein herself states that Carol burns memories to gain the power and energy needed to fight. In that case, Elfnein herself is then a living memory repository for Carol, since all of Elfnein's memory flashbacks shown so far are Carol's memories of happier times with her father.
Some of the song names can get rather...interesting. However, one name in particular stands out, that being Tsubasa and Chris's duet in GX, BAYONET CHARGE. Why? Because a bayonet is a blade that can be attached to a rifle to use as a makeshift lance. The old weapons of both Tsubasa (blades) and Chris (guns) are mixed to create a new weapon; at the same time, Tsubasa and Chris lend their respective voice and Leitmotif to create a new song.
On the subject of Chris, her transformation sequences have undoubtedly gone through the greatest changes over the course of the series. This, in turn, is keeping in line with her development as an individual. In the first season, she uses the same transformation sequence with everyone else because she had almost No Social Skills and thus has little individuality to separate her from the rest. In G, she becomes more accustomed to school life and is a nicer girl overall, and her transformation sequence encompasses Magical Girl aspects as a result. In GX, the Magical Girl theme in her transformation is cranked Up to Eleven, showing that Chris is now comfortable with being a regular girl and liking girly things (which can also explain why she now has a stuffed rabbit on her bag).
In GX, the Autoscorer Leiur has a strange desire to be as "flashy" as possible with whatever she does. It's puzzling as to why she wants this, but when you consider the element she controls and then compare it to the elements of Garie, Phara, and Micha, it becomes evident that she wants to make up for being stuck with the least interesting and versatile of the elements by making a show in everything else. After all, not a lot of people would say that someone controlling the ground is more interesting than, for say, someone breathing fire, right?
GX seems to abuse interpersonal dialogues between the Symphogears in the middle of combat, but once episode 10's revelation comes to light, it suddenly makes sense: the Autoscorers are deliberately antagonizing the Gear users, forcing them to use the IGNITE Modules and letting them overcome their personal problems in order to control it. They want the Gear users to go into the controlled IGNITE mode; they can't recover the Dainslef's 'cursed melodies' if they quickly kill the Symphogears, after all.
Shirabe's new transformation in GX has a brief portion where she stares at the camera. It crosses into Squick territory for some, but consider who she started to hang out with when she started attending school. Yes, the resident Meta Girl Yumi apparently taught Shirabe about how to be self-aware, which is why she stares at the camera in her transformation. In other words, Shirabe has become aware of the fact that people are looking at her naked body when she transforms; so, she looks at them as if to tell them not to stare for too long.
It becomes more obvious when you look at her transformation from G...which was undoubtedly one of the more Fanservice-y ones in that season. Yes, she learned that there were people who saw all that, and from the looks of the subtle Death Glare she gives in GX, she's not happy.
Shirabe's transformations as a whole seem to incorporate more fanservice in her transformations compared to the others, as even in AXZ, where every transformation was toned down in fanservice from GX, Shirabe's has a portion where she cups her hands over her chest and performs yo-yo tricks around her body to manifest her armor. But then you remember that Shirabe is the true descendant of Finé and that Finé was someone who casually lounged around naked and wore thestripperifficNehushtan Armor...guess it runs in the genes?
Chris is actually smarter than she looks, as shown in GX when she shows off her stellar report card to Kirika and Shirabe. However, when you look at her fighting style compared to the other Symphogear users, it makes sense. Chris is a long-range fighter, which means that she has lots of more mathematical variables to consider when shooting projectiles, like trajectory and wind direction. Sure, she can go in all guns blazing, but such a tactic could result in friendly fire. The fact that she can factor in all of these variables in a short amount of time, concentrate in hectic situations, and still hit every target near-flawlessly without putting her teammates in danger shows that her mind had these smarts since the first season. It was only a matter of time before she found out that she can transfer what she learned in battle to school, which is why she can slack off very easily; it's basically second nature to her by this point.
Alternatively, Chris is diligent in her studies because she feels the need to set an example for Shirabe and Kirika as their upperclassman. The GX OVA delves into this a little and it's mostly Played for Laughs, but Chris knows very well what it feels like to try and adjust to normal society after years of being forced to fight for her life, which is why Maria personally reached out to her and asked her to look after them. Helping the two new kids on the block with their studies is Chris's way of getting closer to them without bringing up their past histories.
Dr. Ver's greatest desire is to be a hero despite the fact that his intentions and actions show that he's anything but. Though, you would probably want to go down in history as a hero too if your name was "John WayneVercingetorix".
Chris' big appetite and poor table manners. Considering that she was trafficked and essentially starved for the first half of her life, she probably had to cherish every scrap of food she got her hands on, and things like social etiquette were undoubtedly never taught.
Chris' winter uniform in Lydian. Compared to Hibiki's uniform, it is clear that Chris' is ill-fitting, primarily on the sleeves. Fanon theorem says that Chris would not be able to fit in any smaller uniform (appropriate for her height) because of her large breasts.
On Chris' stature, it is largely due to her being starved for most of the first half of her life and it stunts her growth significantly. Her breasts are due to her foreign blood which, by statistics, result in a larger-than-average bustline.
The fact that Kanade dies after using her Climax Song despite other Symphogear users surviving the attack. Kanade's usage of the Gungnir is artificial and has to be constantly sustained by LiNKER, and before she unleashes her Climax Song, she notes that she hasn't taken enough LiNKER to mitigate the toll on her body. Compare and contrast with Tsubasa and Chris, who have a natural affinity with their Symphogear, and Shirabe and Kirika, who usually take a dosage of LiNKER before using their respective attacks.
Kirika's "Gokuren - Igalima" song from G is a symphonic rock piece that prominently features a piano that plays along with the guitar and other instruments. In her GX song "OVERKILL SCYTHE HELL", however, the piano is absent, being replaced by a harpsichord and electric keyboard while the guitars are turned Up to Eleven, making it sound more like a traditional rock song. Which other Symphogear user is known for having a Genre Motif of rock? None other than Kirika's own senpai, Chris. This likely means that Kirika has found a new role model in Chris and is starting to take after her in more ways than one, which is proven in Episode 8 of GX where she understands Chris's frustrations of being protected by someone she wanted to protect and ends up taking her side of the argument.
In a similar vein, Chris's "GUN BULLET XXX" song from AXZ tones down the hard rock a bit in favor of adding more techno sounds and even featuring a piano in some parts. The piano, as mentioned above, associates with Kirika's symphonic rock genre while having techno sounds is a trait usually associated with Shirabe's genre. Naturally, this indicates how close Chris has gotten with her two underclassmen and how she considers them to be important mainstays in her life.
Alternatively, Kirika incorporating more guitars in her pieces can be seen as her trying out a different music genre now that she's freed from F.I.S. and allowed to do whatever she wants. Starting from GX, Kirika uses her "desu" Verbal Tic a lot more in her regular speech and character songs, and lyrics in the latter indicate that at times she's really saying the English word "death" rather than the Japanese word "desu". Why is this significant? Well, what's the first music genre that comes to mind that incorporates heavy guitars and a death motif? Death metal.
Shirabe having Tsubasa as her partner for AXZ may seem like an odd choice as the two have very different fighting styles, but it makes sense when looking from a character standpoint. Shirabe's fighting style is the most unique of the Gear users as she mostly has her powers harassing enemies from afar while the others either hold tangible weapons (Tsubasa, Chris, and Kirika) or use their fists (Hibiki and Maria) to personally take down enemies. And though Shirabe has her yo-yos for close combat, it's still a far cry from the other weapons and the only other long range fighter, Chris, has to undergo a different style of training because of the differences in weaponry. Thus, it's only logical that they would have Tsubasa do the honors of training her as not only does this go with the theme of the Gear users interacting with different people, Tsubasa has been using her Symphogear the longest and can adapt to different situations thanks to the many years of experience under her belt. Furthermore, training with a partner as unique in fighting style as Shirabe can also benefit Tsubasa's own training, so it goes both ways.
In addition, pairing Shirabe and Tsubasa up showcases that, despite not interacting a whole lot throughout the seasons, the two are Not So Different and even act as foils to each other. They're both the resident stoicdark haired girls of their respective trios and they both care deeply for their teammates despite them not showing it. They also tend to build emotional walls around themselves as a result of wanting to become stronger by themselves so they can better protect those around them, though the difference is that Tsubasa became aloof after she lost someone dear to her while Shirabe is aloof because she's afraid of losing people dear to her.
The same can also be said for Chris and Maria. Both are reformed villains who once fought for their respective season's Big Bad and have since worked to atone for their sins. Their Dark and Troubled Past and questionable actions also come back to bite them on more than one occasion, but whereas Chris often thinks back on her past actions and wonders if she could have done something different, Maria tries to distance herself away from her past because she views her former self as weak.
Hibiki and Kirika are both cheerful, upbeat girls who like eating and are often scolded at for their naivete. They both also have a tendency to act as Stepford Smilers, with Hibiki covering up her problems because she wants to reassure to others that everything is alright and doesn't want them to suffer because of her and Kirika acting like she has no worries of her own because she feels it's her responsibility as the cheerful one to shoulder others' burdens when they're suffering.
It's been noted by many in their interactions after G that Hibiki and Miku have grown closer in their relationship, never hiding anything between themselves and always being capable of getting their message across to each other. While this can easily be explained by character development, AXZ reveals that they were freed from the Curse of Balal when Hibiki removed the Gungnir fragments from herself and the Shenshou Jing Symphogear from Miku. With that in mind, it's no wonder they're suddenly able to relate to each other more easily than before.
Maria has a more silver color when she wields the Airgetlam to contrast Serena's more prevalent white colors when she uses it, something that can be better seen in XDU where both sisters can wield their copy of the relic at the same time. The color for silver (and other similar hues of gray) is the result of adding black to an existing white color or vice versa. Guess which Gear user used to wield a black-colored Symphogear and is now using a white-colored one?
Phara's Sword Breaker, as a philosophical weapon, breaks anything that opponents believe is a sword. Therefore, it breaks Tsubasa's weapons, and comes close to breaking Tsubasa herself since she believes she is also a sword. Fortunately, Tsubasa is able to think past this with the help of her father. However, why didn't Maria just punch Phara in the face like she did with Garie?
In fighting game logic, playing as a fist-fighting character against a sword-wielding character normally puts you at a disadvantage because of the sword's disjointed range. Maria already had a brief confrontation with Phara in the first episode where she didn't possess a Gear and had to rely on her wits and hand-to-hand combat to survive. Based off of that experience, Maria likely attempted to forgo putting herself in another situation like that by using the Airgetlam's Whip Sword and wide array of projectiles to keep Phara out.
In G, it is revealed that Shirabe is the descendant of Fine when she activates Asgard. Why doesn't she use it in GX, then?
Because Fine (well, her soul, technically) died taking the blow from Igalima. Shirabe may be her descendant, but she no longer has any of Fine's powers.
Hibiki's first transformation in season 1 showed us mechanical parts bursting out of her body. This can be explained by the fact that the relic she uses to transform is embedded inside the walls of her heart. The staff at SONG also say that the fragments are spreading.
In Symphogear G, we realize that the fragments aren't spreading, but growing like some sort of tumor. Half way through the season, she has to have the crystaline tumors removed from her body after every fight. It must hurt to have metal bursting out of your flesh.
Chris's lines to Genguro when the latter found her, half-starved in a ruin, indicate that Fine is not the first, or only one to sexually abuse and exploit her.
Shirabe and Kirika's flashbacks to when they were at F.I.S. reveals that they had to undergo painful tests with LiNKER to see if they were compatible with Symphogears. Fortunately for Shirabe and Kirika, they passed the tests and were granted freedom so they could fight. Which brings the question: whatever happened to those who weren't? What happened to those who weren't compatible with a Relic even with an overdosage of LiNKER? We all know what happens when either one of the above two instances happens, so we can only imagine what happens when both occur at the same time...
Really, the thought of having scientists perform unauthorized tests on young adolescent/teenage girls without any parental supervision is enough Adult Fear to think about.
Considering that Kirika and Shirabe are at least implied to be in a relationship with one another after the explicit love confession Kirika makes in GX, another thing to be considered is that the relationship is possibly incestuous. They're both Fine's descendants, after all. Regardless, it's never made clear how closely or distantly they're related, but at worst, they're cousins. At absolute best, however, they're distantly related enough for it to be a complete nonissue in terms of universal morality.
You're overthinking it. Yes, some descendants might have been related but once you hit past three generations people really aren't genetically related anymore beyond sharing a similar ancestor. And considering Fine apparently dates back to Ancient Sumeria, they're likely about as related as Genghis Khan's millions of descendants, i.e. not very.