I was admitted to both Dartmouth and Georgetown in the 2006-2007 application cycle. Ultimately, I choose to attend another private med school on the East Coast. But Dartmouth was my second choice and I much preferred Dartmouth to Georgetown.
Frankly, I loved the rural New England environment. I grew up in Oregon and am an outdoor enthusiast, hiking, camping, snowboarding, trout fishing. All of the outdoor activities that I love are available at Dartmouth. The natural beauty of this area is stunning. I know that I would have been happy at Dartmouth. I also liked the hospital alot. And I liked the proximity of the undergraduate campus. The med students at Dartmouth did not seem competitive with one another but very supportive of their classmates.
If you are an outdoors person who could thrive in a rural environment, then Dartmouth is a great choice. If you are hardcore urban, that is a different matter. OP, it sounds like you really prefer the urban environment of DC, so you need to consider this aspect carefully. Obviously, if you excel at either school, you will have great options for residency.
I would make my decision based on cost factors, and location.
Oddly enough, I am going to med school in a large city. Oh well, it is interesting.