This is a great question. There are two entities with which you can execute a reverse merger. The first is to find an existing public company that has ceased operations and the second is referred to as a "blank-check" corporation that is legally created from scratch.
Advantages of an existing shell:
1. There could be an existing investor community following the stock. Having "built-in" volume is not a bad thing.
2. The public shell could be a holding company of synergistic operations and the reverse merger could have a highly strategic agenda.
3. Often, existing shells have cash, or other liquid assets on hand. Cash could be used to structure the deal and jump-start the new entity.
Advantages of a "blank-check" corp:
1. You will avoid any "skeletons" an existing company might possess.
2. You have complete control over the structure of the new company (i.e. number of shares, corporate charter, etc...)
3. It might be cheaper and faster.
I suppose the best method is circumstantial. Same as in buying a house. If you want to move into a specific neighborhood, you might be forced to purchase an existing home.