We can all agree that X-Men Destiny was not the X-Men game we've been waiting for. It had some good ideas, but it's overall presentation, repetitiveness and it's shortness was what kept it from being truly great in my opinion.
Now for a truly great X-Men game, Bioware would need to make it. Mass Effect and the playthroughs of Star Wars TOR are perfect examples of what they're capable of in terms of story telling, character interaction, and role playing.
I see a Bioware X-Men game like this. Have a new mutant like Shepard where you can pick their background, choose their gender, and adjust their look.
Character creation:Now since mutants can look like pretty anything regardless of what their actual powers are, Bioware could go all out for the character creator such as having the option to go for odd skin color, pointy ears or no ears at all, a tail, fangs, horns, you name it.
Background choice: You would be able to choose what kind of background your mutant has. Are you just a regular person who suddenly has his powers activate and you make your way to Xavier's school? Are you a Weapon X experiment escaped before you had adamantium grafted to your bones? Did you have mutant parents and your powers were active from birth, but your parents were killed by Purifiers giving you a negative view of humans? It's up to you!
Powers: The power section should be less about power selection and more about archtypes. These would be divided up into four categories:
Telekinetic is an obvious powerset and a classic, though it would unlock passive abilities like developing telepathy later on to aid in making conversation choices, tactile telekinetic shield to defend from attacks, etc.
Feral is more in line with Wolverine, Beast, and X-23. It can give you a slight healing factor to begin with, claws, or even the ability to turn into a were-beast form which you can choose to keep active or not.
Energy control can range from having Havok's to Gambit's powers and anything in between. You wou choose one type of energy to control to begin with and have the option to branch out into other energies.
Elemental would give you the power to control earth, fire, generate and morph your body into water, and Storm's powers as an unlockable after you beat the game the first time.
Story: I say a fusion of the various continuities thus creating a truly unique, though not unfamiliar, universe for your character to explore.