Graphically superior to 2007's Tenkaichi 3.
B3's story mode is improved over that of Budokai 2. You get to fly around the world; you can go straight to the next fight, or you can explore, and find some extra cash or capsules (new moves and abilities you equip your character with). Once again you can find Dragonballs. There are 1 to 3 (usually 2) of them to find during every scenario, and if at the end you've collected all 7 of them, you get to choose a reward, such as the Breakthrough capsule, which allows characters to perform all of their moves.
I won't say I'm thrilled about this story mode, though. You spend more time flying around and reading dialogues (the same ones you've had to read in other Budokai games), than you do fighting. The first Budokai game is still the one that did the DBZ story the most justice. If you don't care to explore, my advice is that you just find the Dragon Radar (you'll only need to find it once), pick up the Dragonballs and move on to the next fight; you'll get the important capsules that way.
The story goes as far as the Majin Buu saga. However, you can unlock Super Saiyan 4 for Goku and Vegeta (for instance by equipping Breakthrough). Omega Shenron can also be unlocked.
The fighting itself is lots of fun. I suggest you go through the tutorial first to learn the new moves. For B3, the R1 button lets you transform, and the L2 button makes your character go into Hyper Mode. In this mode the character turns red and its energy is consumed rapidly. You need to be in this mode to perform a finishing move, and also the Dragon Rush. The latter is initiated by punching, kicking or blasting your opponent away from you, and pressing the circle button at that moment. The defender will get three shots at evading your next attack (I suggest you look at some game footage); if he fails to evade the third, you will launch an extra attack (a plain kick or energy blast unless you have a move like Final Flash, Special Beam Cannon or Warp Kamehameha equipped).
Finishing moves like Big Bang Attack, Hellzone Grenade and Spirit Bomb are initiated by launching the opponent into the air using the L2 button while in Hyper Mode. The defender will have a chance of decreasing the damage done if he manages to press the X button at the right moment, while 3 gauges are filled up (again I suggest you look at some footage).
You can also teleport behind your opponent, even while you're going down and an energy attack is about to be used against you, by pressing the X and the left or right arrow button on the D-pad.
Using capsules, fusions like Gogeta and Gotenks are once again available. A thing unique to B3 is that you can equip an Item capsule and use it in a fight by holding the X button while pressing the down button on the D-pad twice. That way you can get an attack or defense boost, or get extra health and energy etc.
B3 differs enough from the other Budokai and Tenkaichi games to warrant its purchase. It's as fast-paced as the Tenkaichi games, it looks great, and better. Going through the story mode to unlock new characters and capsules might be a bit of a drag (you might like it, I don't think it's great), but once you can get into the VS mode with your favorite character, you'll have a blast. Tenkaichi might offer more in terms of battle options, because of its team battles and the ability to start fights in a transformed state, but then, the transformations and everything else in B3 looks so good you won't mind.