It really just depends on what you are looking for in a rock. I prefer dry rock myself, however everyone has a different purpose for what they want out of their rock.
Live Rock:
Pros:
Life outside of what you put in it
An instant cycle
Coralline algae at start up
Possible invertebrates and corals on the rock
Cons:
Much harder to aquascape
Possibility of introducing unwanted pest like algae, crabs, corals, and shrimp
Pricier
A little bit more of a hassle in terms of going to the airport
Dry Rock:
Pros:
Less chance of pest
Makes aquascaping MUCH easier
Very Porous
Cheaper
Lots of holes for your fish/corals
Cons:
Rock takes about a year+ to grow coralline algae
Some will leach phosphate in the beginning if not properly treated prior
Cycling will take much longer
Having to clean the rock off before introducing into tank