I feel weird using the same character across multiple AUs, personally. 

If it's within a persistent story, of course I'd rather have a persistent character, but when it comes to using the same character to fit into all kinds of different stories... I'm not really into it. It makes any character development and experiences that the character has gone through erased every time, and if you're running them in multiple places at once, it is hard to keep straight what they have gone through in each setting. So you can't really use the things that have changed the character naturally in one rp for another rp, because in that alternate world, it hasn't happened at all. Which -if you are like me and think about the character in the current, developed state- is not just insanely difficult, but also feels like a waste.

This doesn't apply to re-purposing an old, out of use character for a new rp.