Much better. Makes Budokai 2 look like a joke.
Budokai 2 had better fighting techniques, and it had more combos, thus making the game a button mashing contest. However, the story mode was horrible, as it was only a stupid board game, and the Dragonballs were hard to get.
Budokai 3 has introduced several new concepts. Such as Hyper Mode, where you go berserk for a while, which is the only way to unleash an ultimate attack. However, if you waste it, you become a wide open target. Use a Dragon Rush, which gives you three chances to deal extra damage.
The teleporting and pursuit abilities are ways to attack and teleport, making the game even more complex. Guarding isn't the only way to stop an attack. You can dodge slightly, and you can dodge to one side.
With these, the story mode is so much more fun. The new way of fighting makes the game even more addicting, and you can only get better with time.