I dunno man, Cyclops' current characterization is pretty fucking straightforward: He's pretty fucking tired of things fucking sucking for mutants and he's gonna do whatever it takes to make sure mutants are not fucked with. With the added wrinkle of being on the run due to the whole "being world's most wanted terrorist for using a cosmic force of destruction to impose his will on the entire planet and murdering Charles Xavier" thing.
Meanwhile, Wolverine has had multiple lifetimes of things fucking sucking for mutants and he wants to make sure kids get a safe place where they're not being fucked with, while trying to get integrated in a world that kinda hates and fear them.
They hate the shit out of one another not only because really they always have, but also because they both feel the other one is a huge fucking hypocrite -Cyke espousing the "whatever it takes" attitude Wolverine was all about for years and Logan being mostly pacific except when kids need to be defended-
It's pretty fucking straightforward, really.
As for Ilyana, Bendis could've made a smoother transition, but having her powers being gigafucked could really justify a change in attitude, though, yeah, the Gillen characterization fucking ruled.
EDIT: GOOF TIME NOW, with the solicit for Thunderbolts #22
THUNDERBOLTS #22
"NO MERCY" Part 3
How far would the Thunderbolts go to deal with Mercy?
Would they make a deal...with the devil?
Or Mephisto, who is technically not the devil?