Canon!Alma is in general, mentally younger. Even though he's an Akuma and a fully grown body, he still only has about two years of experience in life--plus a vague collection of past life memories. He's less understanding about the world, more focused on Kanda, because Kanda was his world. Kanda was his best friend, his only friend, his past lover, and his only peer in a world of torturous tests and books.
Yes, before Kanda was 'born' from the pond/womb, Alma had the scientists, who were very friendly to him--to the point where Twi and Edgar seem to think of the Alma (and later Kanda) as more than just test subjects. But as any lonely child knows, adults are no substitute for other kids your own age.
So Kanda was Alma's world. Supremely important to Alma even before he began to remember things from the past.
However, this is where canon!Alma and Exorcist!Alma begin to differ. While canon was unconscious in a coma for nine years, mentally remaining unchanged until he learns Kanda was searching for Alma's past self the whole time. Alma makes a decision to become an Akuma to hide who he was in the past--but also in a crazed anger to strike at everyone and everything around him. Trying to destroy the Order (again), but mostly focused on Kanda. He wants to get back at Kanda's betrayal--for killing Alma and living on, letting the Order continue their experiments--but also to keep Kanda to himself and stop Kanda from ever knowing Alma's shame and what the Order really did to them both.
And while all of this is very mature and thought out, it's still from the childish, tortured little Alma who's very intelligent but still not emotionally developed enough to accept what's happened--but granted, who would be? Alma is the terrified child and the shamed woman all at once, confused and lashing out at everyone.
He still doesn't quite know how to live outside of the Order, or how to deal with life. His focus is on Kanda and himself, and everything else is just one big mystery.
The Exorcist, however, has had nine years of growing up, not really remembering what happened. He knew on paper--an artificial Exorcist went crazy and all that tried to stop him were subdued and killed. He knew his memories had been toyed with, but looking at the photos of the massacre had made him ill. Especially the note that he had been close with several of the people he killed, including another artificial Exorcist named Kanda.
Disgusted and terrified of himself, Alma grew up hard, not unlike Kanda did. He made friends easier, but was slow to open up to them--scared he might go crazy again, even if he didn't know why he'd gone crazy the first time.
He's still awkward about social things, still childish in many ways, but he's a lot more worldly. He knows other people, he's had nine years to make new friends and grow close to them.
He stayed with the Order because he thought he was dangerous, and was afraid to loose himself on the world--and by the time that thought process had begun to change, he had made too many friends to just up and leave. Friends are very, very important to him, after all.
Of course, the change in his mind was brought about when Allen (helped by Neah's song) brought everyone back from when the Ark had swallowed them up. When Allen brought Alma back, he didn't know about the mental block the Crow had made to lock up Alma's memories, and so Alma was brought back 'whole'--without the damage done by the mental block.
Alma got through the rest of the mission, but went mysteriously missing during the time when everyone was discussing what to do about Allen and the 14th Noah.
The Second Exorcist went out somewhere quiet and destroyed everything he could--without his Innocence that was still being repaired. Then he curled up under a tree and cried for everyone he had killed so long ago.
Alma wanted to just run. Just get away and never come back. He didn't want anything to do with the Order, or the horrible things that had been done to him. But that thought led him to think about the horrible things they'd done to Lenalee, and everyone else--what they were talking about doing to Allen.
So, reluctantly, Alma returned to the Order, realizing his friends were still most important to him.