A close contact english saddle is significantly less secure than say you average western, dressage or Aussie...
I'm not certain that is true. A former moderator, Maura, told me years ago she started horses in a close contact saddle because that is what she has spent many years using, and all her reflexes and balance were based on riding a forward seat in a close contact saddle.
If someone is a total beginner, then a western saddle is probably easier to stay in when things go bad. My Australian saddle - the one I used to stay alive while learning to ride a very spooky Arabian mare - was very secure for a beginning rider. More so than a western saddle! During the first 6 months, the poleys on the Aussie saddle left bruises on my thighs from being slammed into them - but they kept my hips aligned with my horse and saved my butt.
Once I got used to riding a forward seat in an Aussie saddle, I also stopped making contact with the poleys. It just didn't happen during the next 5 years or so. Then I switched to a western saddle...and for a time, I found it harder to stay solidly with my horse. In a forward seat, "security" comes from low heels and the lower leg - not the seat. The wider tree and all the leather under the knee made it hard to use my lower leg the way I had learned.
Switching to this western saddle made it harder still:
The leather is slicker than snot on a door knob. The bucking rolls have disappeared. I concluded they were too small and too far forward to be of much use. Sheepskin - a.k.a. butt velcro - has helped with the slickness, but makes it even wider:
Of course, there are western saddles designed to make it easier to stay on when things go wrong. But HOW a rider approaches riding counts for a lot. For a totally new rider, I think an Aussie saddle with a horn is darn hard to beat for keeping a new rider on:
But I also think a rider who learns English-only may well be more secure in an English saddle, and a rider who learns western western-only may well be more secure in a western saddle. Our habit patterns - how our body has learned to respond in the first split second of a spook - is a huge part of staying on.
I consider myself a western rider now, but I fully understand how an English rider in a close contact saddle, legs all around the horse, could find it easier to stay on in a jump saddle than a western one. I sold my two English saddles some years back. The horse I ride now is a fundamentally easier horse to ride, and I've also learned a lot more about recognizing when things are ABOUT to go bad - and backing off before the explosion happens. I'm thinking about getting another English saddle for use trail riding.
BTW - when people discuss western vs English, most focus on the saddle. I think a bigger difference is in how one is encouraged to use the reins. In English, the more advanced you are, the more you take up contact. With western, the more advanced you are, the less contact is used.