If you're going to release a fish supporting the weight of the fish horizontally is better for the fish. They're used to being in water where their weight is compensated by the water. Probably not a walleye, but with a bass full of eggs or especially large trout, you can actually do damage by holding them vertically. It actually stretches their spinal column holding them vertically.
How many of you have held a big trout vertically and had it start bleeding?
All that said I prefer the horizontal for a picture too.