I doubt prices are going to go down, especially during high season. Bodrum is the premier vacation spot for the Turkish elite and they will keep MO and Aman busy during the summer.
MO is much better than Aman both as a property and location, Aman is a longer drive to the hot spots, but you need to drive in Bodrum to go anywhere so it won't matter that much. Still we are probably talking about the no 1 and no 2 hotels for beach vacation in Turkey so both are very good.
Bodrum is %100 safe, I can't remember any time in my life where there was a security issue there.