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!!
I tend to get on from the left out of habit. But at certain events I am required to get on from the off side, so I try to practice it occasionally. I encourage new riders to get on from both sides as much as possible so they don't end up like me. My body memory makes it feel really weird from the off side...but my horses do okay with either side.
All my horses are freak easy, flighty tbs and one of my paints has been bashed and doesnt even let you get on unless your legged up so I always get on the left... the rest of the horses arent broken in lol...
But the new ones im training atm, ill use both sides so their quite