I'm not sure I understand what your are talking about or not, but it sounds like this is the way Japanese kitchen knives are usually sharpened. It's easy to do -- spend longer sharpening one side than the other.
The extreme example would be called a single bevel knife. Only one bevel is really sharpened, though the other side is touched just a little. The result, in this case at least, is the cutting edge is much closer to the object being cut.
This little ascii diagram might help:
Double bevel: \/
Single bevel: |/
As you push/slice the blade into some material, the following happens:
Double bevel: |\ \/ /|
Single bevel: || |/ /|
If you are chopping a tree branch in half, I can't see how this would help, but it makes a difference shaving off extremely fine slices of something (like vegetables or fish), because one side of the cut -- the side next to the bevel -- is falling away. Hopefully that makes sense.
Another way to illustrate the difference is to think of what a double bevel chisel would be like trying to shave a thin slice of wood. The blade would be going into the wood at a much deeper angle, and it would be extremely difficult (impossible?) to get as thin a slice as with a single bevel chisel.
I don't think knives sharpened this way are "sharper," but they can be used in a way that makes them appear to be so.
Double bevel Japanese knives are typically also sharpened assymetrically, though I don't know the reasoning behind that. I assume it offers a compromise between the benefits of single bevel and the benefits of double bevel.