I don't backpack camp. I truck & camper camp. I bring the bins-o-steel with me. But i also have many combos that would suit you.
Eastwing axe
CS Trail Hawk
Ontario Spec-Plus kukri
A Becker BK9 or BK7 or BK2 or BK10 or BK4 would also do just fine, as would a Condor Boomslang, Ontario SP8, SP10, Tops Alaskan Harpoon & many, many others. The list is endless. Condor is about to release some chopper goodness, called the Warlock machete, Lochnessmuk, & Pack Golock Knife.
I personally prefer a knife type blade for splitting firewood that has already been cut to length. You can baton an axe, but i prefer using a knife. The blade is much longer, i place it where i want it, then baton it. Those who can really wield an axe with precision would prefer an axe. I can not, so i prefer a large knife. Once you use them all, you will have your preference.