Great question. I have both. I have spent a lot of time talking and thinking about this question
If you're tough enough to handle the vibrations, a cyclocross bike with the right tyres can handle everything a commute, an audax, a month long tour, rail trails, fire trail, moderately technical singletrack and a little bit of serious off road. What it can't handle is serious downhill, jumps, or long sections of fast very rough singletrack (like constantly bouncing over rocks or tree roots).
I've done 5 days of genuine mountain biking - 50+km of singletrack and firetrails - on my cyclocross. Every time I was the only person without suspension. Once I was with a mountain biking club, about 20 people with dual suspension, 3 hard tails...and me.
I find I can keep up ok on the smooth, fast flowing singletrack (ie, dirt that winds fast back and forth between trees). I can't keep up on big rocky downhills - the vibrations get too much.
Also, even with two pairs of gloves, my hands get pretty sore by the end of the second consecutive day. Not sore as in "it hurts to hold a beer", just as in, "can we go slower".
So I bought a dual suspension mtb - to be able to go much harder on the rough stuff.
For me, the cyclocross is a great commuter and tourer, great for long day rides (did 130km last friday), and a lot of fun on medium-difficulty singletrack. And I love the sheer perversion of appearing to be on a road bike
But since you already have a road bike, maybe the cyclocross would be too similar. If I was in your position, I'd probably lean towards a hardtail, so that your two bikes are as different as possible. It mostly depends on how much genuine mountain biking you're going to do, and how much you would expect to still use your road bike.
Try this thread