When I can't cook/purify water using a ground fire, I use a DIY tin can Bushbuddy clone I made. I can generally fuel it well with hand-broken twigs and pencil-diameter sticks. If I have the time, slightly larger diameter wood cooks faster and requires less feeding, so I use a carbon steel Mora to chop or split larger diameter wood by batoning it. Peeling or splitting wood can sometimes be necessary if it's very wet. I like the Erickson #1 wood-handled and the red plastic-handled Erickson models, and prefer a carbon steel blade because the edge stays sharp longer than stainless steel blades on other Moras. A laminated blade would also hold an edge well.
I don't use my woodstove enough to tell you how long the knife holds an edge when preparing wood for it. Plus, I do other cutting/carving with it. I do know that I started with a shaving-sharp blade, prepared enough wood to boil two cups of water for five minutes (while cooking rice), and afterwards there was no noticeable change in the sharpness of the blade after using it to baton-chop much of the thumb-diameter wood. Still, part of carrying a knife is carrying the means to keep it sharp. I carry a pen-sized diamond sharpener, but there are sharpening cards which are lighter, and I'll probably switch to one of those soon.