I prefer esf, mainly becuase it is better in terms as far as playing a 3d fighter goes. Also, it's on a pc for one and I don't like playing many console games these days (heck, I don't even own a ps2).
Although The Whole Budokai series is pretty wacky in it's own way and I can enjoy it, I prefer esf over it mainly due to the fighting system, rather then 100+ moves in Budokai and the controller combinations for them (heh, DMZ is sought of like Budokai in that aspect having to use a combination of keys to do some attacks). So you can see, using DMZ as an example to why I don't like it as far as a 3d fighter goes. Sure, using button combinations is great, and can be done a little bit on a keyboard, but it becomes much easier to do on a controller, and that's why I'll leave that style of fighting through the budokai series to the console.
Another thing to also add is that esf is free (as lnog as you own half-life, which isn't very expensive at all these days), and you can expect to find people pllaying it online to paly with where as budokai games don't yet have the feature to paly against others, you could only play with friends and your friend might be a n00b at palying budokai or not very good at playing it, in esf it's a different story altogether. If you find someone to fight on a simlar skill level to you the fight is a nice challenge, and I also consider Budokai to be more complex to learn becuase of the control system.
I think I jsut summed up about what I think on this subject.