I usually mount from the left just because I'm lazy and a creature of habit. Although, the first barn I had my horse at didn't have a mounting block, so I had to mount from the ground. With my short stubby legs, short stirrups, and 16.1hh horse, it was quite an effort! (I know, bad for my horse, but it was only 2 weeks, no flames please!) After a week, my left knee started to hurt from mounting like that. I had to mount from the right and it felt very awkward! My legs were not as strong on the other side!
I generally dismount from either side and sometimes I slide back of his big butt!!