Go to third the runner caught in the rundown might score or be out or end up on third. By taking third you have a runner there no matter what
This is the correct answer
It depends on the game situation if it is the last inning and 2 outs you just lost the game. Since all the catcher does is run the runner back to third at which point someone is out since two players can not occupy the base.
If it is any situation with 2 outs you have just run yourself out of the inning.
ON THE OTHER HAND...if it's the last inning and the game is tied and there are no outs you MUST have the runner go take third and give up the out, you now are guaranteed a runner at third with one out as your worst case scenario (which any coach would take in a heartbeat).