If punchy bas is your thing you can't go wrong with Beats. I have the Beats X which to be sure are the least "bass heavy" and among Beats newest offerings which is actually why I like them. They are bluetooth but have the best sound on a bluetooth I ever tried though.
The last time i checked Jabra Elite 65t are the best choice. I haven't used them. but i got a positive review from on of my friend who is using these one but he has Samsung device and i think they might be good you i series too.
Hi...bearing in mind the basically simple audio circuit in the iPhone, you are never going to real quality bass because it isn't there! However, reasonable quality sound is possible by using "proper" headphones such as Sennheiser HD650.
It also stands to reason that the minute diaphragms used in phones usually used with the iPhone are incapable of reproducing decent bass - in either quality or quantity.