It all depends on what you want as to whether the V6 or V8 is better. If you want handling, the V6 is a bit better--the lower weight of the V6 gives it a near-perfect 50/50 front/rear weight ratio (the V8's no slouch, at 52/48 F/R, but it is a tad heavier). The very few 2nd Gen V6 Sports are reportedly the best handling of all LSes.
If you want a manual transmission, you're stuck in V6 land; all of the V8 are backed by a 5-speed slushbox.
The V6 is marginally better than the V8 on fuel economy, but the difference is small enough that your driving habits will be more important than the EPA ratings.
In general, 2nd Gen LSes have fewer endemic problems than do the 1st Gen LSes (though any individual car can have problems)--aside from generall being lower-mileage vehicles, Lincoln also addressed a great many issues in the '03 redesign. The early '03 V8s had some COP problems, and there's an extended warranty on them. Leaking valve cover gaskets and failed COPS are the most common failings on the 1st Gen V8s (not counting the normal things that go wrong as cars get older); COP problems are relatively rare on the 1st Gen V6es, exceedingly rare in post-'03 V8s, and almost nonexistent in 2nd Gen V6es.
