A cross bike will generally allow you to install full coverage fenders because of increased clearance around the seat stay and fork. You can install fenders on a road bike but if you want full coverage you typically have to kludge something up because of the reduced clearance around the stay/fork/brakes. Important if you intend to do a lot of rain riding.

If you want disc brakes (for said rain riding), a cross bike is more likely to come setup to accept discs.

Otherwise it's personal preference.