The VX is uniquely versatile - good handling on the road AND an @$$-kicker off-road. Hard to find both qualities in one vehicle. You can put low-profile street-meats on it, but then you lose it's trail capability. Mud terrain tires will enhance off-road forays, but will cost you in fuel, acceleration, noise and handling.
My strategy is BFG ATs with D-load rating (8-ply). I can pump them up to 60 PSI so the sidewalls don't flex, retaining cornering ability like a low-profile tire. That also increases fuel economy by 1-2 MPG. The price is an unforgiving ride, so I usually keep them at 46 psi, a good compromise. When off-road, I can air down to 10 psi for excellent traction (larger contact-patch), flotation in the sand, and a very compliant ride. The D-rated sidewalls are inherently stiff even at low psi, so handling isn't scary, and they hold up to trail debris.
My $.02; good luck in coming to a decision.
Rick "Baxman" LaMarche
Supercharged, Dynamated. SCCA Oregon Region rallycross class winner