Use them both dependant on circumstances. Generally if I'm talking about things, I'll use "different from" and concepts are "different than." I have no idea where I got this from or if it's correct, but it is my usage.
And about either and neither, to say "me too" in an affirmative possesion/circumstance i use either, and to deny possesion/circumstance i use neither. Don't know if that made sense at all