It is faster and that is the main reason to do a reverse merger you also have some built in liquidity. Cost I am not sure of right now as I do not keep up on that, a reverse merger is not cheaper if the shell is dirty and causes liabilities and legal problems that is for sure.
Buying an existing shell can be a little more expensive but quicker to do. Creating a public vehicles takes time and has very few shareholders and market makers at the start.