I don't have a ton of experience with these, but my trailer came with a Dometic 15,000 that wasn't working. Ducted central air setup. These kind use a thermostat on the wall. If it is ducted, it will have wall thermostat. This setup often has many differences between Dometic and coleman. Or at least the older ones are different. I replaced my Dometic with a used Coleman 13,500 ducted unit. Due to thermostat setups being different, I had to either replace the thermostat or make a crossbreed. Upon research, my Dometic thermostat had "industry standard" wiring and the Coleman (from same age trailer) had an oddball, almost obsolete wiring which required a special thermostat that was very expensive. The Dometic thermostat can be swapped out for a Honeywell digital home style unit quite easily which I'd like to do in the future. So I made a crossbreed air unit. The upper unit is Coleman. I re-wired the Dometic harness to the Coleman and used the Dometic controller and lower ceiling unit (air intake vent and controller bracket). At this point the computer thinks it is running a Dometic. The upper units are nearly identical. The mounting bolts were off a little so I re drilled holes in the lower mounting plate to accommodate the Coleman up top. It worked out great and works perfect. However 13,500 isn't enough for hot humid Indiana summer weather on a 33' trailer with a 14' super slide. Doesn't help that we have all black leather furniture.
So I just got done installing a second used identical Coleman 13,500 towards the rear. This one is non ducted and they are very simple. All a/c's use the same size roof opening and all are similar in mounting. They all use 120V. If the dealer is giving you the option then they are saying, presumably, that they are going to make sure it is 100% functional before it leaves their lot. So it's brand preference. I will tell you that the older ones (late 90's) that I have, both upper units are nearly exactly the same. The compressors are the same brand and the whole top assembly looks 90% identical between Dometic and Coleman. I am sure newer ones are different. I've heard a lot of people swear up and down that the Coleman's are quieter. Since my Dometic didn't work I can't comment on that, but from what I've seen of the construction of the two, I do not see any reason for one to be quieter than the other.
That being said I am now quite happy with my setup. 27,000 BTU's = reefer trailer :-D definitely make sure you get a 15,000 BTU unit. I would honestly say the true power output and/or options you can get out of the deal should influence your decision as much as popular vote of brand loyalty. Maybe you have a 13,500 now but if you go to coleman you can upgrade to 15,000. Or maybe get one with a heat strip. I don't know. If its all apples to apples on the unit size maybe see if they'll let you pay the difference to upgrade to a larger one or to add a heat strip (if you wanted) I'm sure they'd be happy to do that.
Sorry this was long winded but perhaps it'll put you at ease about it. A lot of each brand are out there in use and I don't think one is much better than the other. Both brands have been in the RV industry a long time and you might hear one preferred over the other but honestly I can't say I've heard much bad about either. I did do a lot of research looking for Differences between the two when preparing to replace the ducted one.
1988 SunLite Hideaway 9.5' TC project
1996 Ram 3500 Cummins dually highly modified