Definitely an axe for me. I'd be confident in a knife providing almost equal service IF I had confidence that the areas I were in were mostly untouched. In my experience, coniferous forests tend to have a lot of dead wood on the ground and dead standing wood, giving ample fuel that can be split down with a mora.
I made the mistake of assuming that would be the case on a trip a little while ago, but it was towards the end of summer and the smaller wood had all been picked clean over the year. Luckily, it was a car-camping trip and I had an axe and saw (a couple axes, actually). I don't go into woods I stand a chance of getting lost/disconnected in without some kind of axe, even for a day trip. I definitely wouldn't go into a forest for a couple months without, say, a boy's axe and a saw. One wet day of trying to use a knife (even a big knife) to buck and split 6+ inch logs would probably convince most of the logic in this.
That being said, there are extremes and experience/skill is no exception - an axe will always be more effective for lots of wood processing than a knife, but someone with no axe experience might be better off with a big knife just for safety's sake - but if you don't have any skill with an axe, my personal recommendation would be don't go on a 2-3 month hike through the woods. Similarly, there's folks out there with enough experience and skill to do with a pocket axe what many of us couldn't easily do with a felling axe.
All of this assumes that a decent amount of firewood processing is necessary. Plenty of folks do long backpacking trips with no fires, which of course makes all of the above irrelevant. For me, I'm not going to hike 10 hours a day for 3 months, so camp comfort matters quite a bit and a fire is up there.
So... preference, experience and needs all need to be considered.
