What are the pros and cons of having a development team working on site versus remotely on a game?

Communication vs expense.

Communication underpins everything else, the time to fix problems/bugs that arise, the time to train new staff, the effectiveness of teamwork, the amount of re-work or duplication or throwaway work that's done, team morale, etc, etc... All of this is improved by having people sitting near each other and able to talk face to face.

On the other hand, renting an office, keeping it running, and relocating staff to it is incredibly expensive compared to remote work.

On-site is particularly efficient when you need to iterate and discuss problems often. If the scope and breadth of what you are doing is known, or if you're willing to forego complete control (or yet again, if dealing with a small team and exclusive positions), offsite is much less expensive.

That said, offsite is only advisable if you have something strong in place that serves the purpose of communication.

This can range from having meetings through Skype, up to having proper task management (and comments!) software.