Mmm, just saying that's sort of what they're designed for is all. I know I want to jump, but do I have a jumping saddle? Nope, still looking for one that'll fit my horse that I can afford. So I'm stuck with a cheap and nasty little AP that's way too small for me.
A dressage saddle is for riding on the flat only, which means it's great for trails or if you know you don't want to jump. They are usually more comfortable than an AP saddle until you try to jump. Then your lower leg goes out the window and you tip forwards, and no matter what you do it's just a million times harder to jump in a dressage. I still do, but only over small stuff (as in crosses that are MAYBE 6" at the point where Monty likes jumping them).
An AP you can ride on the flat or over fences up to about 90cm, so it's brilliant if you can't afford two saddles, or if you aren't sure what you want to do. Most beginners ride in these and most riding schools use primarily AP saddles on their horses, because it's too much work to find a jumping saddle that fits your horse only to find that you don't actually enjoy jumping, and ditto with dressage saddles.
Jumping saddles are designed for jumping. Depending on the quality of the saddle in question, some put you in a horrible chair seat and others put you in good alignment but are open enough to allow you to move your leg forward for landing or if you're riding a horse that's liable to refuse. Usually if you're going to jump more than about 3" you'll be jumping in a jumping saddle, and I know a bunch of people who don't jump that big but who ride exclusively in a jumping saddle, because they are designed exclusively with jumping in mind and therefore make it far easier to jump WELL.
By the way, my AP is very flatwork-oriented. Relatively straight-cut flaps, very deep seat. It is almost impossible to get out of for jumping but it's the best I've got. Well, I have an AP that is more jumping-oriented (forward cut flaps, shallow seat), but it doesn't fit my horse, AND it's still an inch too small for me!
It's just my opinion of course but I think that an AP is a much better choice for a child than a dressage saddle. When they start jumping, it's all they want to do, and if they're in a saddle that makes it harder for them, they're going to resent that and demand a new saddle. At least that's my experience, and what's happening with me! (although I'm the idiot that went and bought the dressage saddle in the first place, even though I knew I love jumping... LOL)