03+ have a slightly stiffer ride with more road feel, but also have much improved steering response with the rack and pinion (over the -02 recirculating ball)
The spring rates were unchanged, the shocks were changed to standard monotube with the rears moved outboard of frame rail. The front swaybar was made smaller and the rear unchanged. The shock valving was toned down a little for 04 because of NVH complaints. The front lower control arms were switched to stamped steel for 06+ for cost cutting and further reduce vibration.
The 03+ do not have better braking. The 98-02s stop in shorter distance than 2003+
There was a 4hp increase over 2001-2002 w/ duals thanks to the knock sensor which allowed more aggressive timing. Though, because of the 03+ increase in weight despite the power increase they are slower than 01-02.
03+ includes standard dual exhaust and 3.27 RAR, -02 had single standard w/ 3.08 though duals were available on sig/cartier/limo as well as a 3.55 RAR on Tourings.
Take a look at this link:
http://moldyrabbit.com/liquid/changes.html#03
Though it's for Vics, most applies to the Town Car as well.
IMO, it's personal preference. I love the look of the 98-02 Town Cars, the 03+ still look nice but not as sharp IMO.