A tri channel motherboard with four RAM slots? That seems very odd, is it some kind of cut down X58 board? Are you sure this isn't a natively quad channel motherboard, IE an X79?
Tri channel 12GB will offer a little more bandwidth/performance than dual channel 16GB if you don't use the extra 4GB offered by the dual channel configuration. If this is a quad channel motherboard, than you can have quad channel 16GB which will outperform the tri channel 12GB at all times.
Also, consider this: Increasing channel count/memory frequency/lowering latencies doesn't have a large impact on most software anyway, so you probably wouldn't be able to tell the difference unless you are using some memory bandwidth sensitive work (such as archiving) often.
If you want to use 16GB, then get it. If you won't use even the full 12GB, then don't bother getting 16GB.