How high do you plan on jumping?
I don't jump so I may get this wrong...but I think jump saddles are designed to be ridden with shortened stirrups and a forward seat. That is needed for higher jumps - maybe over 2'6"? I can't find my 1940s cavalry manual, but I think that was the height where they recommended shortening the stirrup.
An AP saddle should be OK for lower jumps, if it is a jumping AP. That sounds odd, but AP saddles are sometimes adapted from dressage saddles, and sometimes from jump saddles. So some AP saddles do OK with low jumping, while others do not.
My English saddle is a jump saddle that I ride on the flats with long stirrups. My horses seem to like it, and I do too if I trust the horse. But then, I've always ridden with a bit of a chair seat - which may be why my daughter suggested nicknaming me "Harley"!
Remember - I don't jump, so this may all be bogus! It comes from reading, not doing.