The trigger wouldn't be my make or break decision between these two models, as you could easily drop the same Geissele trigger into the V11 on your own.
The bigger things to think about are weight, rail length and the barrel. --Assuming that you would be getting the 18" V11--
DDM4V11 - Weight: 7.43lbs - Barrel: Chrome Moly Vanadium Steel, Cold Hammer Forged, 1:7 twist, 18? S2W® Profile, MP tested, and Salt Bath Nitride Finished - Rail: 15" Keymod
DDMK12 - Weight 7.41lbs - Barrel: Proprietary Blend of Stainless Steel, Cold Hammer Forged, 1:7” twist, 18? MK12 Profile, Salt Bath Nitride Finished, and HP/MPI tested - 12" 1913
Turns out the weights are really similar, so not a big difference there I thought it would be larger. Generally "stainless steel" barrels are considered to be more accurate, but that isn't always the case. I don't have experience with either of these rifles to give a personal experience based opinion. I do have 2 other DD rifles that shoot well. Lastly is the rail. First thing is the length, the extra 3" on the V11 covers the gas block if that matters to you and also allows more rail space. Second decision about the rail is 1913 or Keymod. 1913 is your standard quad rail that DD is so famous for making. I haven't seen the keymod in person, but I would assume it is up to the same standards. This will effect the type of attachments you can put on the rifle. I think this is one of the bigger differences between the rifles.
To touch on the trigger again the Geissle SSA is a great trigger. I have one in one of my rifles. You can usually get them for $185-210 depending on where from, so factor that into the price difference of the two rifles. If you think that you don't want to start with that trigger, then there is no issue with using the mil-spec one on the V11. Once you get used to it you can decide if a nice 2-stage trigger is something that you want.
I'm not going to make a recommendation of which one I think you should get because I think that each person has certain things that they prefer over others and I don't want to give a biased choice between two good rifles. Hopefully some of the above facts will help lead you towards a decision of which rifle you like more.