Adaptational Context Change: The robot-to-fistfight duel between Kouichi and a resurrected Yajima is present in both versions, but their only similarities are the participants, the leaping out of their robots to collide their punches and that one of the robots is Apparition. The everything else, from the cause of the fight (it's not about Risako's happiness in the manga) to its location (a stormy night on a coast in the anime, bright daylight at Juda's base in the manga) to the outcome (Kouichi "wins" in both cases, but instead of a What the Hell, Hero? speech, they reconcile then and there) is different.
Worthy of note is that, in the aforementioned L, Shinji Ikari is Kouichi's kohai, and ends up becoming one of his best friends. It's quite interesting if you think about it, since both of them are EXTREMELY messed up kids and their series both show two very differant, realistic reactions of giving an unstable child the power to destroy the whole world.
Differences Between the anime adaptation and the manga:
Kouichi is already Linebarrel's factor in the manga at the start. He's not a whimp being bullied, he's more of a gang leader of sorts. He doesn't spend too much time using Linebarrel pre-JUDA due to on his first time piloting it, fighting Reiji, who proceeds to "show him true violence". He doesn't pilot it again until Yajima is killed.
Yajima ends up siding with JUDA and works as an black ops operative for them, working behind the scenes.
Yamashita (Hind Kind's Factor) is a boy. Yes, he's a dude. No really, the anime actually changed him to an androgynous girl for whatever the fuck reason Gonzo wanted to do that for.
Soubi and Talisman. This is the biggest change and the one that really divided fans of the manga. Volumes 5 and 6 (which occur BEFORE the Kiriyama coup, remember this) are all devoted to his very tragic backstory and well-written recruitment by JUDA. The anime didn't put it in at all.
It's not an alternate dimension where the Machina come from, but actually a dark future where they've basically gone out of control and sentient. They also live on the moon now and the Earth may or may not have been reset a few times before the manga started thanks to the Machina. Emi, Katou, and Soubi all come from this future.
Miu joins later on in the manga, post-Kiriyama coup. She's....mentally unstable, to put it lightly. Also, Painkiller forcibly makes Miu its Factor, and is much more sinister in design.
Jack doesn't defect to JUDA's when Reiji betrays JUDA to side with Kiriyama. That was Gonzo being Gonzo. Also, there are two Katou generals who appear multiple times early on who never got animated. Kiriyama himself is actually outsmarted by Reiji and his father, who decides to appoint Reiji as the successor to Kiriyama Industries, not Eiji Kiriyama, his own son.
The Reiji betrayal arc is much different as it was actually Reiji being a mole for Kiriyama's father. Everyone at JUDA picks up the hints and puts things together pretty quickly. The true scope of Reiji's and Mr. Kiriyama's plans don't become evident until near the end of the battle against Kiriyama.
Kiriyama is spared and vanishes for a time before returning as The Atoner in a fashion reminiscent of Balzac.
Doymuji isn't a military cadet going undercover. He's just a classmate of Kouichi who sort of becomes a civilian contractor for JUDA until he gets his own Jinrai much later in the manga. Plays a major role in convincing Soubi.
Demtri is killed by Kiriyama's Jinrai pilots and this fact ends up coming back to haunt Kaitou's forces as Satawari (with a more subdued personality and unkempt hair) turns on them for having the killers among their ranks. He ultimately ends up a wild card in future struggles