I also switched to a safety razor a few years back, and I didn't notice any change in the likelihood of cutting myself. It's possible that I have particularly resilient skin or steady hands, or something, but our dueling anecdotes seem to cancel out.
I've been using safety razors for a while now, and my personal experience has been that it depends on two things: the geometry of the razor (the tool, not the blade), and the brand of double-edged blade. I have used blades and razors where I can wantonly hack away at my face without fear of harm, and I have used combinations that require the utmost concentration if I want to make it out of the bathroom alive. If I had to guess, I would think that you two just have very different setups.
