It depends on the quality of the remake and what I'm looking for. For some games it is nice to simply see a facelift. For other games, I prefer it when the really change things up.

I've been playing the Steam version of the FFIV remake lately. I got the DS version back when it came out and beat it, but I haven't touched it much since then. So it's cool to rediscover how much effort (in my opinion) they put into building the game from the ground. I also like how they changed some things up to throw off veteran players, like altered boss tactics.