It is interesting that you brought this up. I have been looking (slowly) for a new Town Car for a while now. At 330k miles, my '86 isn't what it used to be.
I've had a few different trains of thought on this. One consideration is that I have always used my Town Car as the towing/traveling/camping rig, and I often carry bicycles, canoes, etc on the roof rack. Neither Thule nor Yakima list support for anything after '97, and I haven't gotten my hands on a newer model to see if something could be made to fit. I do have a rack that fits my '97 Mark, so if the roofs are built similarly, I'll bet I'd have an answer.
Stylistically, I prefer the newer (2003+) grille, and I know at some point (2006?) they cleaned up the instrument cluster considerably, and added a digital speedometer. My '86 has the full digital dash, and I rather like it.
I have also heard that the later years had some significant cost-cutting. Still, since they are no longer manufactured, I doubt I'd be too picky. if I had my way I'd probably shoot for '06-'07. Since cost is the critical factor for me, I doubt it will be anything quite that new.
Re-reading this lead me to another thought. My Town Car is also my winter vehicle here in Minnesota. One of the reasons it does so well in the snow is that it has a surprising amount of ground clearance. I hadn't considered until now that some of these newer models may in fact sit lower. Probably not much of a concern..
