Before comparing beaches or nightlife, check where your flights land, because this pair is not served by the same airport. Bodrum uses Bodrum-Milas Airport (BJV), about 40 minutes from Bodrum town. Marmaris uses Dalaman Airport (DLM), around 95 minutes away. Driving from Bodrum-Milas to Marmaris is possible, but at about 131 km and around two hours and 40 minutes it is the long way round.
So if you have already booked flights into one of the two airports, that may settle things. If you have not, read on and choose the place first, then the flights. It is worth doing it in that order: a holiday spent in the wrong kind of resort is harder to fix than a slightly less convenient flight time, and the transfer from each airport to its own resort is short and simple.