I've just spent about 10 minutes on Google trying to find info on these models. There is a website called bikez.com that used to have specs and info on every model, but they've loaded it up with ads and pop-ups to the point where it's practically impossible to use.
What I would do if I was you is call up your local Honda dealer (or go down there) and talk to someone in the parts department. These guys never fail to amaze me. Someone who's just hung around a dealer for a few years picks up an incredible amount of information.
There were two engines made for the Shadow, they look the same but are different inside. When Honda began making V-twin cruisers they made the engine balanced so it would run smoother, but they found that a lot of people wanted the single-crankpin engine like the Harley has.
The Harley Davidson V-twin began as an experiment, with a second cylinder grafted onto a single-cylinder engine. The two cylinders share a single crankpin. One connecting rod is forked, to connect to the crankpin on either side of the other connecting rod, so the two cylinders are lined up, not offset. (This is sometimes called 'knife and fork connecting rods'.) So the engine is actually a split single cylinder.
This is NOT a good way to design an engine, but Harley's been making them like this for over 100 years now. This is why they vibrate like they do, and why they make that 'potato potato' sound when they idle.
Honda put the two cylinders on different crankpins so they could be timed 180 degrees apart for better balance and less vibration. But then they found that some bikers prefer the Harley arrangement because it has 'character'. So Honda came out with the Shadow ACE (American Classic Edition) which has the single crankpin. I've ridden one of these and it is very reminiscent of a Harley, though physically smaller. The vibration is more, but it's not objectionable. Twins generally vibrate more than 4s, but the vibration is at a lower frequency so it isn't as annoying as the buzzy vibration of a badly-tuned 4 that makes your hands go numb.
Anyway that could be the difference between the DC and CDA. You might ask if either or both are the ACE version or not.
As for which I'd buy, well I'd rather not have the ACE myself. Other than that I'd buy the one that was the best deal for the money--lowest mileage, best taken care of, etc.
I have a Honda (a 1993) and I love it. It's got about 65k miles on it now and it's needed no work at all so far, not even a valve adjustment.