A razor polished edge will be better for push-cuts. A coarser edge is better for slicing. You can convince yourself of this easily: get yourself some 3/4" hard poly rope. Slice it with your razor-polished edge -- it will skitter along the top and barely cut at all. Now take a few passes of that same knife on a medium or coarse stone and try again -- now it bites and cuts deeply. There are some materials -- especially harder materials -- that really require a coarse edge to cut. If you replace the hard poly rope with manila rope, coarseness doesn't matter as much, because manila rope is so soft you can push your polished edge right through it. Note that I'm using rope just to illustrate the principle, not suggesting that rope-cutting is a particular important application for most of us.
A polished edge will be more robust and last longer than a coarse edge. The coarse edge has deep scratches that form micro-serrations and little stress risers, these get bent and broken more easily than a glass-smooth surface.
The edge strategy I use will overall outcut either a fully razor-polished or fully coarse edge. What I do is razor-polish the entire edge. Then I take the knife back to a coarser stone, and take a few light strokes on the part of the blade nearest the hilt (where the serrations would be if this were a partially-serrated blade). Now I have a polished edge along the belly, but when I run into something harder and tougher, I can cut it along the coarser part.
For self-defense, I would advocate worrying less about edge coarseness and more about edge angle -- a thinner angle can significantly outcut a thicker one, by many times to one. I feel that most people make the mistake of leaving their edges too thick, and leaving way too much performance on the table. Many of these pre-set sharpening doodads leave you at 20 degrees per side or higher, and that's way higher than a good cutlery steel requires, especially if it's strictly for defensive use.
Joe
