I have a variety of horses in that respect.
I have a “zero stop” mare. She is the absolute confidence builder of confidence builders. She is scopey, brave, and I don’t think she’s ever so much as looked at something I’ve pointed her at. She’s gone through the 1.40m and literally anyone could jump her around that height. You can eat it at 1.40m and she will simply adjust her halo and get you over it whatever it takes. She packed my young teen daughter over her first ever 1.20m and 1.30m classes this summer and I’ve never seen a kid have so much fun. She is the epitome of “zero stop” to me. The key is that she WANTS to do whatever it takes to make her rider happy. The trade-off is that she’s not ‘freaky’ clean. She typically jumps around double clears, but if you eat it, she thinks it’s ok to pull a rail in order to bail you out. And that’s the biggest difference between her and the next horse on my list…
I have a “will stop if you f up” mare. She doesn’t tend to look at jumps (though will peek every now and again). We’ve shown through the 1.30m, but I’m careful with her because I know if she feels worried or insecure, there is an objection in there, so I try to never put her in a position where she needs to bail me out. She wants to jump, so I don’t ever worry that she’ll stop for no good reason. But she thinks it’s more important to jump clean than to jump, so if she perceives that the jump is going to be ugly and require her to touch a rail, she would rather not do it (though she is freaky athletic, so can extract herself from sticky situations, even when the fences are big).
I have a “best teacher” mare. She will stop if you ride her to the bad spot and drop her. But keep your leg on and she will BAIL over any height any distance any jump (I have an amazing video of my daughter absolutely eating it into a 1.20m 1-stride where the mare achieves unicorn status, lol). But the stop will show up even at little jumps if you don’t ride. She brought my daughter up through the levels and absolutely taught her everything a horse can teach a kid. Like the others, she wants to jump, so she’s not looking for reasons to stop (and doesn’t ever do her rider dirty, and also doesn’t spook). She’s like a tattle tale to the trainer - “hey teacher! Look! Susie took her leg off right there…”
And then I had a “stopper” gelding. He was a chicken, and ended up moving into a hunter life where he is happy as a clam (and no longer stops). He was spooky and it was impossible to figure out what he would be spooky about ahead of time. He showed through the 1.20m, but just got unhappier and unhappier despite loads and loads of scope. As a jumper, he just didn’t want to jump.
I did have one horse many years ago who was a “zero stop” horse in the “absolutely no self preservation” way. That horse was scary, and we did wind up in 2 jump/falls as a result. I always wished he had a little bit of self preservation. I do think that mares tend to be able to balance the “never stop” with “also don’t kill us” things at the same time.
I think there are trade offs all around. The “never ever stops” horse is usually a trade off for freaky clean. Freaky clean is usually a trade off for “ultra brave”. For me, what I care about the absolute most is a horse who WANTS to jump. Beyond that, it’s really about tailoring to what the horse needs from the rider. But WOW does a horse who “wants” to get you around make a big difference in confidence to just about every single rider on the planet!