When I was taking lessons 15 years ago (God, I'm old!) our teacher wanted us to do the perching/crest release type of jumping. She said it was because pressing your hands into the horse's neck was the only way to make sure you wouldn't catch them in the mouth.
It's just a different philosophy I guess... Although I think you're less likely to fall off doing it the classical way because it keeps you centered over the horse. That's the way I jumped - Not really on purpose, it was just what my body wanted to do. My teacher harped at me about it, so I started opening my hands in the air so the horse could take more rein if they needed it and that seemed to satisfy her.