I've done both methods. Live rock back in the day from Harbor Aquatics via Fiji flown in over night, maybe two day air, wrapped in wet newspaper. Some really good looking rock, sponges, algae, and lots of stuff alive that I didn't know what it was. So it looked really great, little bit of die off, and it was grand. Of course there was a small hitch hiker or two that I didn't really want along the lines of crabs but nothing I didn't find fun trying to capture. To this day that was some of the best rock I've ever purchased and it had its own cycle pattern. What was interesting is about 6 months into the rock into the tank I started to get some Sargassum algae that I never saw before. That was really cool stuff that reminded me a lot of kelp. It was grown on some of my lower level rocks and reached up to and floated to the surface. This sort of bio diversity you won't get using dry rock. You just won't see it - it isn't there.
Having said that I just completed a cycle using 150 lbs of dry pukani. A rather nice looking rock, various sizes, with BRS shipping me some that could be used for my front yard landscaping. Ok, I'm kidding. No, not really - a few pieces are extra huge but I don't mind because my tank is 30" tall as well as deep so it fills in nicely. While this is all grand again here is the deal. They are bare rocks. There isn't anything on them. They are dirty, they need to be pressure washed, they need a bleach bath, they need more rinsing, more dosing of lanthium chloride, more rinsing, pressure wash, and did I say rinsing again? Yeah - ok, you get the idea. Some people use acid baths - which removes rock which you paid for (amount varies but some report 5%, some 12%, others 25% or so). But with the bad comes the good. You start with a clean tank, nothing introduced, and you become little Miss Mother Nature, pretty much a bad ***, and create your own bio diversity. It really is a neat process starting from artificial saltwater, dosing ammonia, and waiting. Then testing, taking notes, and following what we call the nitrogen cycle. Then comes diatom blooms, hair algae blooms, and a host of other stuff.
So - both are cool and I think everyone should do both at least once. Chances are if you are in the hobby long enough you will. Now, having said that, and just completing the dry pukani rock I will say this now. I personally will never go this route again. I like the rock but what I find myself doing is going back to what I had before or users of TBS rock and how those rocks look. Then factor in I'm an active scuba diver it doesn't help at all. In time, over the course of a year or so, my rocks will look a lot alike what others have. That is the process. I see it happening now. The rocks I carried over from my 40 breeder with fish, corals, rock, and some sand boosted the life on the dead rocks.
So now it is just a waiting game and I need to sit back and enjoy the ride. Both work. Both are cool to watch and experience. My suggestion is make a list, write down some pro and cons of what you are looking for, and then see what your pocket book will allow. I don't think you will go wrong with either personally so just find what works for you.