As Bill mentioned, duplicate content doesn't trigger a penalty. There are filters in place to eliminate duplicate results from within the SAME SITE but technically not across two sites. What can happen though is that one site will rank higher than the other for the content and you could end up with the wrong one ranking (if there really is a "wrong one").

That being said, I could point to thousands of situations where the same exact content shows up in multiple positions within the top 10 (think news sites syndicating articles), so it's not a guarantee that either site will take a hit. You can let both sites be indexed without too much worry as long as the entire pages aren't complete copies of eachother (which could result in a true penalty if caught...but not just because of the duplicated content), all the way down to the template. Ideally, if you really want to do it right and give both sites a shot to rank, they should each have some kind of unique value add that would serve the visitors in a way that there shouldn't be a reason to get flagged for a penalty.