The biggest change is that many enemies get additional armor, shields or barriers. This means you'll have to far more often wear those down so that your powers will work on the enemies. On higher difficulty levels you won't find many unprotected enemies that just have one health bar, most will have at least one level of armor, shields or barriers.

The damage the enemies cause is also increased, staying out of cover is very deadly on the higher levels.

The minigames are not changed by the difficulty level.

I haven't noticed anything really resembling some kind of AI, so I don't think that changes either.