How much battery do I need?

offroader,

If you think of power in terms of watts, then yes, a 3S system will be as powerful as a 4S system, if both systems are setup to do the same amount of work.

Not all brushless motors can handle the same voltage. Motors have limitations in terms of how many rpms they can turn before tearing themselves apart.

Although some advocate running motors to higher rpms, I like to keep my setups at around 30,000 rpms. This makes for cool running no matter the ambient temperature or terrain. I run Neu motors, which are arguably the best motors available right now. A 2200kv motor on 4S or 1700kv motor on 5S is a pretty solid setup.

In answering your question, the two systems that I referred to will run about the same in terms of speed, but the 5S system will run cooler, because it will draw less current.