I'd think a 7" quality knife can handle any light chopping. If you're going to do extensive/hard chopping or splitting, a hatchet might be a good tool to have.
If you're worried about the price, get the Gerber. The main difference between the Gransfors and the Gerber is the profile. Gerber axes are much thicker behind the edge than hand made axes. They may not be so well suited for delicate tasks. But if you're carrying a knife as well, that's really not a problem. They split firewood very well. I would not worry about the quality of the steel. It's there. And the coating, of which significance is arguable, is very tough. I guess the secondary grind (at least) could be reprofiled, but this would be laborous. I'm not sure if there would be significant benefits.
The
Back Paxe is very light (under half a kilo) and the belt sheath is very solid. And you'll never have to replace the handle. I have to believe they are indestructable. I saw the Gerber/Fiskars axes endure long term hard use in the
FDF. The handle also allows a comfortable high 'choke' grip, if you need to whittle something or make kindlings. I've found some traditional woodel handles to be very uncomfortable when holding them close to the head.
The handle is very short though, and I have seen the larger
Camp Axe sold with the same belt sheath. The heads are the same size, and the larger model is only marginally heavier. If the length is an issue, but you'd still like some leverage once in a while, I suppose you also could fashion a wooden pole and stick it inside the hollow handle and secure it through the lanyard holes.
I'd also suggest checking if
Hultafors axes are sold where you live. These are hand made and seem to be of high quality. Around here they are sold for about the same as the Gerber/Fiskars axes.