I have the newest highest level Braun (don't know the number) and it does a fine job. Nothing like a blade though. Initially as close but nowhere near the staying power. Have you tried another razor, say the M5. I haven't cut myself with the actual shaving part yet (2 nicks with the stupid trimming blade). Some people, i'm afraid, just shouldn't use the headblade. It's great if you have a nice smooth round head, but if you have any ridges, valleys, etc. that's when it gets you.
Thanks to everyone for the advice. I think I'll go with the headblade based on what I've read here and elsewhere. It seems like a good place to start. I've read that the key to making that work is to not apply too much pressure when you are shaving with it.