Both grip size and grip texture really matter to me. I have smallish hands and tend to sweat a lot, so semi-cord grips are a must.
And thickness does matter. One time I dropped my driver off to have it regripped at Golf Galaxy while out running errands. I picked it up later that day and didn't think much about it. The next day at the range the grip felt awkward. I was losing a lot of shots to the left (hard fade).
I took the grip off at home and not only had they left the old tape on, but they actually added two layers of tape.
So I began replacing the grips myself after that.
Standard grip size for me.