Bates and Alyssa are both suffering from post traumatic stress, but how the two handle their stress is what we'll discern.
Bates is Claustrophobic, how? Once you remember that he was Buried Alive alongside his sister, if we assume he was buried in a separate coffin, that might be the reason why he died first ;Allen and Phillip got to him too late. Bates was conscious at that time all the while he was suffocating; he carried this fear until he died and until he got the chance to possess his sister. He doesn't hide because, it's either he doesn't realize his fear or he's too proud to admit it. Similarly, you could say that he doesn't evade because he "'avoids physical confrontation."'
He is just as afraid of his stalker, much like Alyssa. To confirm this theory, if you pay attention, you'll notice that Bates prefers to shoot and kick his stalkers. The survival knife is not considered a weapon and its main significance is to get Ending E, where he stabs a bound and helpless Allen, but he doesn't gut or slit throats with it.
Alyssa may not know it, but she has a dysfunctional relationship with her family. She yearns for her father's love despite being neglectful, her uncle and aunt are terrified of her, thus adding confusion, and she withholds Bates's compulsive attitude. It doesn't help that the reason she might be bullied is because of her weirdness.
If Alyssa Hale is the reincarnated Dan Barrows, then doesn't that make her more powerful than Bobby/Bates? What if Bates knew all along of his sister's potential, and he's secretly controlling her, then the magic from the milicana might not come from Bates but from Alyssa.
The amulet that Allen gave Alyssa is a placebo. Alyssa may not know it, but she actually has the power to push Bates away. Allen must have been dumbfounded that it actually worked. The amulet is just extra will power; this item is the key on how she handles stress. If she doesn't have it, then she loses faith in herself after winning a panic event, letting Bates out.
Now let's compare Bates's and Bobby's behavior:
Bobby is the inferior twin brother of Dan. He relies on Dan's power to move through spaces; nevertheless, he is more free to do what he likes. It inverts with Bates, who's trapped in a body he has no control over; Alyssa's will power prevents him from coming out. So whenever he's given a chance, he lets his boredom out. His actions had horrible consequences to his confused and unwilling sister.
Bobby may not be powerful, but he's cruel and sadistic. His idea of fun and play is to mercilessly stalk and kill his step-siblings. Bates and Bobby are thrill seekers.
Bobby and Bates are callous and fail to heed caution. Once they face a competent or a Genre Savvy "victim", their foolishness can lead to their demise. As soon as you realize this, Bates's promise to Alyssa is rather empty as he can get her killed 3 times.
Bates and Bobby are both neglected. In Bobby's case, it's 'not loved enough'. For Bates, he was hated by Allen and resented by Alyssa. He practically raised himself, and his behavior is still that of an angry bored child.
It's left ambiguous if Bates genuinely cares for Alyssa. But Bobby sure cares about Dannote Then again it could be justified, more on this later., and went after Jennifer to try to avenge him. If you remember Ending C in The First Fear, it implies this. So it's not so much of a stretch to assume both Alyssa and Bates had a good relationship before. It's just the factors on how they grew up.
On the opposite side:
When Dan was born, it was already decided that he was to be worshipped by whatever cult Mary belongs to. It implies that Dan is the more powerful twin and therefore a more revered demon. This is actually more obvious if one finds the hidden painting in the library.
Dan is more calculative, unlike Bobby who clumsily kills partly because it amuses him. Dan shows competence but not skill; however, you could excuse Dan's sloppy attempts of murder by remembering that Dan has always been kept and doted on by Mary, while Bobby was free to wander and do what he pleases, like murder his step-sisters.
Dan also tried a different tactic, manipulating others for his own gain as he maintains his facade of an amnesiac reserved boy (or at least tries to). Bobby couldn't do that for aesthetic reasons. While Alyssa's shyness is not a masquerade, she has no experience in manipulating people.
However, Alyssa must have learned her shy personalty, albeit a self-taught personality. The clue was that the Maxwell family always buries the "'twins"'. This means that Alyssa must've been a sociopath in her previous incarnations, just like her brother.
How Alyssa Hale learned her personality may have something to do with:
1. Unlike Dan, her previous incarnation, Alyssa was not treated with adoration. Instead, she was neglected due to Allen's poor parenting and feared by the people who knew her origin.
2. The only person she communicates with is either her father or Bates. Both are actually manipulating her for their own ends. Allen, at that time, only saw her as a tool for revenge, while Bates is more motivated by getting his own body. In short, with these constant messages, she grew up quiet and meek.
3. Bates has always been inside of her. According to the wiki, Alyssa could sense power. She must have dormant abilities and inept skills, only for her to interpret it to belong to her evil side. The dark impulses that she's feeling could be an interpretation of Bates' sadism as well. She doesn't snap because she believes she's doing what Bates wants. It doesn't help that she has become a timid girl at this point, which makes her prone to bullying. Alyssa eventually starts to develop her sense of right and wrong through her confusion and upbringing.
Now let's compare both siblings:
In Bobby and Dan's back story, we learn that Bobby cannot live without Dan's presence, as it was through Dan's power that allows both of them to remain alive. Dan was able to find a way to escape his predicament by making a body inside his body, thus enabling him to leave the Barrows mansionnote Even though his freedom is short lived., while his brother died permanently now that Dan is gone.
If you apply this to Alyssa and Bates, the mere fact that Alyssa's alive may have something to do with Bates' capability of possessing her. Bates must be consuming Alyssa's power to sustain him.
If my theory is correct, then this would make Bates very Genre Savvy. He's actually encouraging Alyssa to be dependent on him, while he tolerates her defiance. Since he knows of Alyssa's power, he has to keep her on a leash. He makes sure he's extra nice to Alyssa, and only her, because Alyssa could have the power of permanently expelling him out of her body without her knowing it.
The irony is that this time it's Bobby who wants a body to escape his predicament. Since Dan/Alyssa is capable of living without his/her brother, Bates cannot do anything about it. That is, unless he becomes the dominant one and absorbs Alyssa, he could potentially use her as a battery.
So in a way, if Alyssa died instead of Bates, and Bates has a living body that his sister possessed, would she really be the same or could it be that Bates will be the one singing a different song? What if Alyssa proves herself to be a much bigger threat?
So with the Downer Endings of Struggle Within note technically it's a Downer Ending and the Drama CD. This has always been bugging me...but what happened to this girl?