There is a 99% chance that the 1600MHz RAM was working at 1333MHz since, 1600 is mostly OC profiles speed. Which would be achieved only buy changing the Voltage and the timing or profile.
The point to be checked would be the 1333MHz working speed, timings and voltage, if it matches the 1600@1333 speed, timings and voltage they'll be fine together.
Compare the Make and Models spec sheets of the 2 RAMs and you'll be able to find that out.
Secondly, to make best use of the RAM and the CPU, you need to check the RAM allocation table of the Mobo, will 3 sticks be better than 2 or slower.....?? Or will 4 sticks be better than 3.... compatibility wise...