I've got Live 2003 on the PS2. Bought it this weekend. I really like it. I prefered Live over 2K2 last year because it was easier for folks that don't play it often to get in the game. It's more arcade feeling, but I don't really mind. Generally, if both people are somewhat familiar with the game, most games are going to be close and fun. The new freestyle control is interesting, although I haven't mastered it yet. I still just sort of mess around with it. The online mode is great. Lag rarely shows up, and 4 out of 5 games will appear to be lag free; as if you are playing with someone next to you.
If you liked Live 2002, you'll like this. The pace is sped up a bit and the new animations are great. Plays actually seem to somewhat useful now.
I haven't played 2K3 yet, so I can't compare. I'm sure it's good too. But, if you like Live, you'll like the new one as well.