Something I never considered until reading this post, having perfect pitch. I'm sure it would throw a person having perfect pitch and having a different tuning.
Although I am far from having perfect pitch, it is pretty good. I can tune a guitar and get darn close without a tuner. I can also hear someone play a chord and most of the time I can get it right without seeing it.
With that said, it has never bothered me tuning down a half step. It has also been pretty easy to transpose on the spot, I think it helps that I play guitar (six string) as well. Several times I have played in three piece bands with keyboards, so playing in different keys (plenty of flats as I recall) has never been a problem. Sure, when you first start playing with a guitar tuned down, it might be a little weird to start with, but it clears up quickly, at least for me.
As is evident with all of the replies, more than one way to approach this.
Personally, it is easier for me to just tune down a half step. The group I play with doesn't rehearse, doesn't have a playlist, and always manages to throw in a handful of songs I have never heard before, so it's just easier for me. One less thing to think about on a busy stage.