I'm biased, I think. I lived in Colorado for a year just after college. It happened to be one of the happiest years of my life, which I attribute to being able to hike amazing mountains, do positive, rewarding work, and being exposed to a lot of vitamin D.
The GDMBR tends to go through the mountains rather than over them. I prefer being in the mountains, but not with a 75 lb. bike.
Of course the elevation might get you if you're not acclimated but overall, I have to say that I would take two Colorados over one New Mexico. Here's why:
The roads are well-maintained.
The forest service roads that you ride on the GDMBR in Colorado are usually packed down and treated with magnesium chloride to prevent dust or they are fairly compacted gravel. Read: like butter. The only exception I can remember is a sandy section before Del Norte, and it wasn't long.
The mountain passes are almost all at railroad grade.
Sure, the little hills inbetween may be steeper than railroad grade, but there aren't a lot of punishing rollers, and the long passes are manageable. The only passes that stick out as outliers are the pass before Steamboat Lake and the pass out of Radium. Even then, not impossible.
The scenery is great.
Much of the national forest you pass through is still that, forest. In other states, this land has been used for other purposes like natural resource development or ranching. It was nice to be in some pristine forests. Exceptions were the superfund site just after Indiana pass in southern Colorado, but even that was awesome to look at.
Well-stocked mountain towns.
Steamboat Springs, Dillon, Breckenridge, Salida.... They all have restaurants, bars, good grocery stores, outdoors gear stores, and artist shops. If you were looking for a break from the rough life along the GDMBR, Colorado is there for you. It's more expensive in town, but chances are you know someone that lives there, right?
Well, my time with the Internet is up, and my phone is doing strange things with my picture files, so I'll wrap it up.
I guess the only other thing I'll say is that I detoured to Boulder and Denver, and it was rad. It gave me a chance to get off the fire roads, ride some singletrack, see old friends, and unwind a lot. I also met a bunch of fellow GDMBR riders in Salida which was really amazing. It's about the experiences you share with people, right?