The 3850 and 4670 are about the same in performance. The 4670 would use less power and run cooler. You didnt mention any other system specs, but as the previous poster stated, you might be better off getting a new system, depending on what kind of processor you have.
Even if you buy the copy of Vista, the total is around $550 for the first system or $440 for the second, and both would give you a much better gaming experience than you could ever hope for on that P4.
I upgraded my older P4 3.2Ghz system with the 3850 a couple months back. It DID offer a small extra bit of performance, being what I think is the best (?) AGP card available. The previous bottleneck comment is, unfortunately, true however. The P4 can only keep up with the card to a point. Only really worth the cash if you have a truly outdated card.
Recently however, I spent approximately $460 (before shipping) building this new PC, and it's easily 2x faster than the old P4 rig. If you can stand using the current card a while longer, might not be a bad idea to save up for a new system altogether. Plenty of *very* good, and inexpensive, components are available nowadays.