If I need to take off any major metal I'll use a heavy file. For keeping the edge relatively sharp I have an puck shaped axe stone from Gerber. I haven't tried yet but I imagine the heads are very hard so the stone should be as fine as I'll go. The Maul doesn't need to be shaving sharp to do it's job.

for the axe I'll do the same but I'm going to try to put a more refined edge on. I might try running it through my Sharpmaker once I've filed it and gone over it with the coarse stone.