Never touching the surface vs never going underground? Both have benefits and drawbacks...
Surface fortress:
+ food diversity
+ plentiful supply of animals and fishing resources, as well as water (if you have a river or brook, otherwise water/fishing isn't much better than cavern lakes)
+ wood is almost infinite (assuming you embark somewhere wood exists)
+ farmable land is plentiful
+ trade caravans are easy to use
+ pastures for grazers are almost trivial to make
+ military can be outfitted with wooden shields, crossbows (with quivers and bolts) and leather/bone armor within a year if you get on it quickly
+ don't have to worry about dangers of the undergound such as cave adaptation and cavern beasts
- hard to build big structures, especially safe ones
- water freezes in winter unless you are in a warm location
- werebeasts can cause a lot of trouble, especially early on
- weather can cause a lot of problems, especially in an evil biome
- stone and metal are harder to come by, and by extension you will be limited to crossbow/wrestler squads until you buy materials/weapons from the caravans
- magma can't be had unless you embark on a volcano
- generally harder to protect your dwarves
Cavern fortress:
+ Cool, often powerful and predictable beasties
+ Easy to secure your base
+ structures can be dug out rather than built
+ don't have to deal with weather, so it can make evil biomes much more manageable
+ stone and metal are plentiful, so your militia will be much stronger when you get it built properly
+ far more likely to have access magma
+ aquifers can be an infinite source of water that never freezes
+ don't have to worry about sieges, thieves or ambushes from other civs
- wood is less plentiful than you may want
- fishing and hunting resources severely limited with only cave wildlife to supply meat and fish
- grassy pastures for grazers less available
- aquifers make building harder
- you will only be able to trade with the dwarven caravans, and even then only if you find a proper location in the caverns
- farmable land is much less available apart from the first soil layers, and you only have the "dwarven" underground crops available
- always the same sorts of creatures, so far less variety than you can find above
- might be a bit of time before you can properly outfit your military
- cave adaptation can be a killer if you ever need to come back up to the surface or have an exposed area of the fortress
- generally not as interesting as keeping the surface open