There are 3 basic types of English saddles- dressage, jumping/close contact, and "all purpose." An all purpose saddle is more or less a hybrid of dressage and jumping, with some of them leaning more towards one discipline than the other. For small jumps, an all purpose saddle is generally fine, but as you move up in height and complexity, a jumping saddle becomes a requirement. You can also do some small jumps in a dressage saddle if it doesn't have large knee blocks (though many of them do!), but I find it to be pretty uncomfortable to do so.
A poorly designed saddle of any of these types will put you in a poor (chair) seat no matter what length your stirrups are and will make you feel like you're fighting to keep your balance all the time. I find this effect especially apparent when you're in two point (jumping position).
“The horse is a mirror to your soul. Sometimes you might not like what you see. Sometimes you will.” - Buck Brannaman
"Nothing forced can ever be beautiful." - Xenophon