Advantages of using road tires over the big noisy mud and sand tires are a smoother ride, more even tread wear and better handling on wet pavement. A set of correctly selected road tires will cost a lot less, even for top of the line premier road tires.
Road Tire Disadvantages
Should the vehicle need to be driven through the swamp or deep mud, the likelihood of getting stuck and bogged down is much higher when the vehicle is equipped with road tires.
All Terrain Tire Advantages
The all-terrain tire advantages are just about the same as those of standard road tires. Tire performance on pavement is greatly enhanced, especially handling on wet pavement and some off-road activities. The all-terrain tire has only slightly larger lugs than standard street tires, but the lugs are just enough to help with getting through semi-rough terrain.
All Terrain Disadvantages
The all-terrain disadvantages are noise on smooth wet pavement and the possibility of uneven wear from street driving (all the turns).
Finding the Best of Both Worlds
Ideally, you want an all-season/all-terrain tire for your 4X4. These tires have enough traction for rain wet roads and can still pull through shallow sludge one might find in a woodland's trail road.
Road tires can be put on a 4X4 vehicle. An area that can be an issue, however, is finding a tire that will fit the rims on the 4X4 vehicle. Categorically speaking, the tires on a 4X4 are generally not muddles or sand tires---most come with all-terrain type tires. All-terrain tires are produced in standard sizes, so unless the vehicle has undergone an after-market upgrade in extra large rims, standard road tires will fit just fine.