I had been searching Craigslist for an Adams Trail-A-Bike for a while now and recently found a 1997 model that had hardly been used. I talked the guy down to $50 which I figured was a pretty good deal. I have someone delivering it this weekend (it is coming from out of town). Like I said, it is an older model, and therefore does not fold.
I have a folder, we don't often fold it. Whatever you decide, check them both for recalls (05 and earlier, I think, had bolt problems). The 97 could even be upgraded to the current model hitch if you want.
I would personally go with the newest model you can afford. We had a 2006 Adams and just bought the very same model, but this years (2010) version and there are lots of little things that make the newer one much nicer and more comfortable for little ones. I know from looking at a non-folding version and comparing that to my 2006, that there were an equal number of improvement there.
Also consider if you will want to transport it in a car at any point. We do a lot of riding around our home, so don't need to fold it. But sometimes we load up in the car and drive to a neighboring area and bike there for the day. Having the folding option is crucial for transport. These things do not load on a bike rack well and having the ability to fold them and put them in the trunk of the car is really cool.
I am relatively certain that the oldest models need a replacement hitch due to recalls and I think that some of those actually require a hitch different than what Adam's currently offers. I "think" that they are no longer producing that retrofitted hitch and you would need to find someone that had one in left over. Seems like I read about someone having trouble getting the right thing on another board.
Before I made the decision I would call Adam's for the hitch info, but also check online. I have found that the representatives at Adam's don't always know what they are talking about and I normally make 3 separate calls to ask the same info, just so I know I am getting the correct story. (they are a call center and most of them haven't ever used the product!...yes I asked)