Yeah, '99 and 2000 are great. I enjoyed the striker system. I never got the hate. I think '99 might be my most played game in the series. I played that non-stop for months when I got it sometime around 2000/2001. It might be my favorite, or at least real close. But I like them all. Well, maybe not 2001, mainly because of the abysmal presentation. Hah. It plays well enough, though, if you can get past that. Oh, and XI is amazing. I should really play it more. I really enjoyed tagging in that and 2003.
Anyway, here are the differences I can remember between the Dreamcast and Neo Geo versions of the games.
KOF '98/Dream Match 1999: Dreamcast version replaced all of the original 2D stages with polygonal versions, replaced the original soundtrack with an arranged version, and added some gallery features that made use of the Neo Geo Pocket link cable to help unlock preview images of '99, among other things.
The Dreamcast version unfortunately stops and restarts the music every time a new character enters a team match, which was not something that happened in the Neo Geo original, though it does not affect single character mode play.
KOF '99 Evolution: All stages were replaced with polygonal versions like in the previous game, but these are highly animated and constantly change during matches, so you'll see thing such airplanes land and depart as you fight. There are also a few new stages, I think. All are much better executed than in former game.
More strikers (such as alternate version of characters, Vanessa and Seth from 2000, and Fio from Metal Slug) were also added under an Extra Striker option. The original soundtrack was also replaced with an arranged version.
KOF 2000: Added an arranged soundtrack (the original might be selectable, but I'm not sure at the moment), tons of extra alternate strikers (one for each character, I think?), and classic stages and music from other Neo Geo games in versus mode. A sliding art puzzle mode was also added into the Gallery Mode.
KOF 2001: Added a versus puzzle mode, and I think a Gallery Mode. I don't recall any other changes at the moment.
KOF 2002: Added a Shingo and King as playable characters, and I think it added a Gallery Mode. I can't recall any other changes right now.
For '98, I'd also recommend the PlayStation 2 Ultimate Match version, which includes the new version of the game with tons of new features, and also includes a perfect port/emulation of the Neo Geo original. There's also an Xbox 360 version, but that version lacks the new stages, the Neo Geo version, and is also only in Japanese, for some reason.
For 2002, I'd recommend people just get either PlayStation 2 or Xbox version (which includes 2003, not available on Dreamcast), or the Unlimited Match version for PlayStation 2 (Japan-only) or Xbox 360. Both have more characters and other extras than the Dreamcast version.
There's also a Japan-only The Kings of Fighters NESTS Hen compilation that ported both the Neo Geo and Dreamcast versions of '99, 2000, and 2001 to PlayStation 2. 2000 and 2001 also had their own unique PlayStation 2 ports that were bundled together in the U.S., which are different from the Dreamcast versions.