I assume you are talking about MTB + CX bike vs MTB + road bike.
The differences between CX and road frames most pertinent to your situation in my estimation would be bottom bracket height and brake type. CX bikes have higher BBs so they can clear obstacles. Road bikes have lower BBs which gives a lower center of gravity and tends to make the bikes more stable in a straight line. In fact, some bikes go a little lower than most (Rivendell et al) for even more stability.
Most road bikes have caliper brakes and most CX bikes have cantilever brakes or V-brakes. Some bikes of both types use disc brakes. Disc and cantilever brakes give more room for wider tires and fenders than typical short reach caliper brakes, but some road bikes are set up to use long reach caliper brakes which allow wider tires.
If I wanted a bike for road riding with the capability of slightly wider tire, say 35mm, for rougher roads and dirt roads, but not offroad, I would probably go for a road bike with long reach caliper brakes and a low BB. In fact, I did. My Salsa Casseroll has long reach caliper brakes, will fit up to 37mm tires (though I run 28), has a low BB and rides like a dream all day long.
Touring bikes take it a step further with low BBs and either cantilever (or V) brakes or discs and heavier duty frames designed to carry a load on front and rear racks or in panniers.
What you choose should depend on what you want to do on the bike. There is some overlap between what the different types of bike can do and what the excel at. That can make the choice more difficult, but maybe less critical.
Confused enough?
