They are just visually different, damage is same for all of them, one hit kill until 36. Ice is my favorite.
Fire punch hands down. In the higher rounds when no longer a one hit punch after ound 35 it will save your life. When you land a punch at these high rounds it will not only slow down the zomboes but the zombies thay you hit cannot damage you, they will swing their arms but wont cause you to get hurt The other punches such as the ice punch will slow them down but if they swing at you before they die then you will get hurt.
Every punch has the element of the staff level 1. So, if you have the windstaff, when you just shoot, it blows zombies away (or stuns them on higher rounds) and when you punch, it has that same effect. I personally think the wind is better because it stuns and blows them away, great if you get trapped. And, buys you time without being hit like the other staffs to use your upgraded staff's special ability.
yea fire punch all the way. if you get cornered stun them they cant hurt you then blow em away with a charge of the wind staff