Which is more informal?

Neither/nor is never informal. The real question is, what's different about Alex? Why can't you just say:

None of my friends care about their future.

If Alex really is so important, and you want to keep it informal, you could say

Alex doesn't care about his future, and none of my other friends do either.

or slightly less informal:

Alex doesn't care about his future, and nor do my other friends.