A while ago, during my Master's degree, I saw a fellow student using a drawknife to shape the legs of chairs. I admired her competence and the elegance of the tool. (See some of her pieces here.)
A friend of mine has inherited many tools from his grandfather. When I saw the drawknife, I asked if I could borrow it. I soon realised that it is a tricky tool to master. Even a very slight change in angle can change drastically the way the blade bites into the wood. I tried to make the same stroke multiple times, and each time had a different result. Partly because of my human error, partly because the action of the blade on the wood also depends on the direction of the grain within the piece.
It worked fairly well to taper a dowel; there were only a few times when it grabbed more than I would have liked. When I started using it to soften out the edges of my rectangular pieces, there was more trouble. I found it worked well in a certain direction, but as soon as I turned the piece around to do the other side, it would grab and splinter the edge.
I think it depends on the way the piece was cut. In the picture above, you can see that the fibres are angling outward against the direction that I was pulling the drawknife, so it's obvious that splinters would happen much easier.
To finish rounding the corners, I ended up using a rasp, which is much easier to control.