My current riding horse is my 21-year old Paso Fino gelding. He's gaited and VERY smooth. I constantly bareback on him at a walk, trot, and canter, but he doesn't gallop because he doesn't know he can (some gaited horses are like this) so I've obviously never galloped him. I've ridden him on my own since I was 7 years old, and he has extreme separation anxiety for my mini mare. I've almost cured this on my own, but not quite. It used to be that if I gave him an inch of free rein, he would take off bolting towards the barn, where his mare was. Now I've got him to where I just have him on a medium-tight rein and he's mostly fine. Still working on that. He's the alpha out of all my horses.
I've ridden our MFT, who was a big boy and needed a firm hand, and our high-strung OTTB in 3rd grade.
I've ridden my mom's boyfriend's 7-yr old TB ex-racehorse and according to his excercise rider needs a very confident, experienced and focused person to ride her.
I rode a Shire from the Amish when I was trying him out to see if I wanted to buy her. She was three years old, greenbroke, didn't know how to neckrein and tried to take off every few minutes. I handled her really well according to the seller, but that could have been a line haha. He had a very choppy trot.
I ride primarily Western, but I took lessons for English for the experience in second grade and rode English on the aforementioned mom's boyfriend's TB mare. I galloped her with no stirrups because, riding English after a long break from English riding, I lost my stirrups and was galloping without stirrups lol! I didn't even feel at a disadvantage......I have a good grip on my seat. I have to when my Paso makes extremely sharp turns while I'm bareback, trying to get back to the barn....he rarely does that anymore from reinforcement that he needs to listen to me when I ask him to.
My parents tought me to ride both disciplines. My mom was on the equestrian team in college and is really a good rider. My dad was the cowboy rider type lol and always corrected me as a five-year old on my seat and hands if they were more than an inch off of perfect :).
Jumping....I never have, but am getting jumping lessons with my Paso from my friend who's on the IEA team soon.
I'll try to get a video....I don't have many, and my English riding isn't that good, but my Western and bareback I think is pretty good, IMO. Here's a really bad video, but it's the only one I have right now: