I own a cross bike and a dual suspension mtb. When the crank broke on my cross bike I decided to throw slicks on my mtb and use that for commuting.
-It Sucked-
It's not a cheesy mtb either. Full lockouts on the fork and rear shock and about 26lbs(which is considered pretty light for a full squish). Going uphill into the wind for 5 miles is no fun. Even going downhill isn't as fun...feels pretty slow.
I've never felt that my cross bike failed me commuting. I have actually taken it on some mild fireroads and it does fine. For anything a commute can throw at it, I think it's pretty bombproof. Even in the winter, knobby tires and a mtb have nothing on a cross bike with snow studs. Hell when the trails all freeze over and are covered in snow, people around here put away their mtbs and pull out their cross bikes. That should tell you something! (Granted we aren't riding the same trails)