Interesting. I have very thick stubble and my Braun does give a pretty close shave, obviously not like a razor but pretty darn close.
Do you know if you have to replace the head or any other parts after a period of time?
I think you are supposed to replace the blades every 2 years. I haven't bothered replacing mine yet, it was crap from the first time.
Your's is probably a foil-type razor, whereas mine has rotary blades. I should probably try a foil-type shaver next. I think different skin/hair types respond better to different shaver types.
The big problem with mine is that it doesn't catch the hair on my neck (perhaps because the hair grows parallel to the skin), so I end up having to go over it several times. By the time I'm done, my neck is covered in blood and too sensitive to touch, and it stays like that for at least 24 hours. I really wouldn't recommend the experience to anyone.
If I had to judge the razor based on the way it works on my face, I would have no problem recommending it. It provides a very close shave (not perfect though). It's quick and easy and there is no discomfort at all. It's just a pity that on my neck it's completely different.