After reading this site for a good month now the one question I always ask myself in this situation now is...

Can I find a better time to get his money? or is this the best shot I wil get?

In this case I would have folded. Neither of you was in rough shape at the time. As you mentioned you had the same stack size so this was a decision with your tourny life on the line.

However if you were short stacked I probably would have pushed also looking for a shot to get back into the game... and similairly if you had him out stacked 3:1, or something like that, I probably would have pushed here also looking to knock one more out and have a nice stack of chips and momentum heading into the bubble.

But in the situatuion you mentioned.. 3rd and 4th big stacks, 2700 in chips still, I would have looked for a better spot to get all my chips in the middle.

Ideally I would want to see the flop with a middle pp and hope to hit my set before all my chips went in though.

Just my thoughts.... if you give us more info though ie blind lvl, what your table was like, read on the player pushing etc I'm sure some of the pros would be more inclined to coment not to mention could give you a more educated answer.