Depends on the application. I haven't found a pair of fingerless gloves that don't leave me with blisters on the webs of my thumbs, so when I'm riding urban or touring I prefer a thicker tape for more cushion. Likewise with my mountain bike, I prefer Ourys to the thinner offerings out there.

When I'm distance riding without a load, for some reason I really like thin tape. Don't really have a good reason for it though.