I commute on my cyclocross bike.
It is tough and fabulous and I certainly feel safer commuting on it than I did on my mountain bike. I can get away from bad situations quickly, I can go faster when I need to, and the bike responds quickly if I have to dodge something.
As far as sturdiness, I've ridden off curbs and on various hazards without damaging the rims or steel frame. My tires are tough and have put up with me blithely riding over broken glass and metal shards so far. If you need tougher or fatter tires, buy tougher or fatter tires... not a whole different bike than the one you like.
Knobby tires are actually more dangerous than smooth tires on asphalt, due to the lowered contact area. (you are only on the tips of the knobs)
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson