I prefer to take a large knife like the SH or BM. They are able to perform multiple tasks of cutting and chopping all in the same package. The last time I went into the back country I used a Steel Heart to do everything from chop large wood for the fire, carve much thinner branches to help get the fire started, open food packages, and even help hold a very hot titanium pot I was boiling water in. While an axe could have done some of that just as well it would not have done all of it as well. I am also of the school of thought which thinks a knife is a better defense tool should the need arise.
Bottom line is that you will never regret having a good knife around, and an axe could simply be dead weight.