I think there are just too many possibilities here. One consideration might be that a large axe will generally both split and chop better than a small one, but if you plan on backpacking with it, a large axe may not be the best choice. A versatile single axe for backpacking will most likely differ in size, from an axe used in the backyard.
All that aside however, I think the best fit would probably be a felling axe of your preferred design. The Woodworking axe to which you point is a carpenter’s axe, and while it will get the job done, it is generally not used for either felling or splitting. A felling axe will do adequately well at splitting and of course chopping. How well it performs at each will depend on how you grind the blade.
The Michigan pattern that killa_concept showed above is a good example of a felling axe. The pattern itself is not that significant. I happen to like the Dayton pattern, many others like the Jersey or Rockaway patterns. It is the shape of the bit and cheeks that most influence the characteristics of the axe. I think killa_concept explained it well. The best tutorial on axe re-profiling that I’ve seen is that done by Paul, and you can see it here:
http://woodtrekker.blogspot.com/2011/04/guest-post-how-to-reprofile-axes-and.html
If you are looking for a medium size axe in the $50 range, you can check out the
Husqvarna Traditional Multi-Purpose Axe or the
Council Tool Hudson Bay Axe (not the best balance). If you are looking for a full size axe in that price range, the Council Tool Jersey or Dayton pattern axe of the desired weight would be a good call. While Fiskars axes are not to everyone's liking, they will do fairly well at both chopping and splitting.
Some good information is contained in
An Ax to Grind, which was put out by the USDA, and the accompanying
video, part of which killa_concept put up above.
Also, judging by the promotional materials, it appears that soon we’ll be
blessed with some additional information on the subject. I burn with anticipation.
http://woodtrekker.blogspot.com/