My understand it that if changing out a Dometic for a Coleman or vice-versa there is a problem with the t'stat wiring. I'm thinking (UH-OH) that the Coleman units use a five wire set-up and the Dometic uses a three wire set up. Or it could be the other way around. I believe that either unit will fit the 14" x 14" opening as that is sort of standard within the RV industry, so many items will fit that size opening.
You don't list the year of your RV, but if it's a newer model, Thurman is correct. You may get lucky and be able to pull new T-stat cable in the place of the existing cable if it's a pretty straight run.
Salem 29RKSS Pushing a GMC Sierra 2500HD!
Gotta go campin!
I'd like to say this: "BamaRambler" statement "You may get lucky and be able to pull new T-stat cable in the place of the existing cable" could very well turn out to be true. The total lack of quality I have seen while working on different RV's will lead me to say that I doubt that the wiring for the t'stat is stapled anywhere along it's route. I think that it would be very possible to pull in a new t'stat cable using the old cable to pull with.