Here's my $.02 take it with a grain of salt.
Live rock: yes you will get the seeded bacteria to kickstart your biodiversity and bio filtration. However, this comes with access dead organisms lodged or seeped deep into the rock where we can't see and slowly leeches out into the water introducing excess unwanted side effects. Yes you get a little surprise with organisms that hitch hike like sponges, stars, worms, feather dusters, but you also may get bristles, nudi, aptasia, etc that are malefactors to our tanks.
Dry rock: I tend to separate this into 2 sub categories. 1. Dry rock that was once live from the ocean or an existing tank that was cured/acid washed, treated then left to dry for a long period of time. This to me is more middle ground. You have benefits and hope that the curing process killed and depleted a lot of the unwanted organics. However, how sure can you be? There will always be organics that has seeped deep into the rock. The difference is that the treating process has extracted a majority of the unwanted live rock organics. 2. Dry rock excavated away from reef source such as arc reef. These rocks have had no marine organism interaction, life, death affecting it. Arc reef claims they cure, treat, and drill all their rocks. They claim with scientific testing that all their rocks have been treated and will not bring with it harmful chemicals or organisms.
Pros/cons:
You lose the biofiltration and biodiversity initially going dry. However, you get nothing you didn't intend to put in there to begin with. Cycling naturally fish/fishes is faster with live rock. However, you can use live sand coupled with dry rock and jump starters like bio spira, dr Tim's 1 and only, or fritz on dry rock to seed the initial nitrifying bacteria that will bond to rock and sand and begin their proliferation.
I have researched and personally seen complete dry rocks from marco in reef tanks that caused algal and diatom blooms. However, they usually have a common denominator underlying issue. Cycling with lights on too long or too high intensity, adding livestock too early believing manufacture and internet claims their tank cycled in 5 days, etc.
My advice, go with what you like best for your build budget. With the resources and research knowledge you acquire, be prepared to spend the time and know what may be potential issues.
I would go dry rock like marco or arc reef with live sand bed no more than 2" deep and no less than 1/2". Seed with fritz turbo 900 add ammonium chloride (please follow manufacture directions and don't just eyeball), let it cycle until nitrate spikes then falls to a measurable zero (we are never certain it is absolute 0), then test for phosphate and let it cycle a couple weeks more until that falls to measurable 0 or close to it. Before adding livestock, I would probably seed with coraline algae in a bottle, add copepods and chaeto, dose phytoplankton, let that whole thing run a couple more weeks to establish the pods population w/o falling prey to feeding fish predators.
Keep in mind, I would do this all without lights on at all except fuge light for chaeto growth. The amount of time you give the bacteria to grow will be 1.5 months total which will establish. Couple that with the copepods and chaeto and coralline algae growth, the biodiversity shouldout compete nuisance algae like diatom, gha, bubble, byprosis, and dinoflagellates. If done right the biofiltration established will keep your new livestock healthy, happy and hopefully disease free.
From here upkeep and husbandry is up to you.
Again, my $.02 and I have not seen anyone doing this exact technique so it is hypothetical based on research. I will be doing this exactly with mybreefer 350 build in the near future.
