In the third installment, you can unlock additional difficulties by beating the game on 'Very Hard'. The first one is called 'Z'-difficulty where enemies gain better AI and stats. Beating the game here unlocks 'Z-2'-difficulty, which adds more of the same. And finally beating the game here unlocks the final difficulty 'Z-3'. This is a difficulty where the opponents all have maxed out stats and a a near Perfect-Play A.I.. Everyone from Raditz to Gotenks will be a nailbiting fight because Computers Are Fast.
Especially Gotenks: The fight with him is between him and you playing Gogeta. The kicker? Each of you have unlimitedki. Teleport Spam will ensue, and failing to be the one giving the kick at the end of a long session of Teleport Spam could mean you end up losing 1/5th of your health to a Victory Cannon. Beat him and you will feel awesome, and be on quite an adrenaline rush afterward.
Of course, there's also the Bragging Rights Reward if you do beat the game on 'Z-3'. A capsule aptly named "Savior of the Universe"
How is Future Kid Buu defeated in Shin Budokai - Another Road? A family Kamehameha involving the Sons of both timelines. Including Future Bardock.
Finishing any Budokai 3 story mode gives you the ending credits, which is essentially all of the major fights in Dragonball Z, spanning years... All to the tune of "The Ultimate Energy!" note except in the HD rerelease, which has an entirely different soundtrack due to issues elaborated upon in the YMMV page
The cutscenes in the original Budokai lovingly recreate key scenes from the anime in glorious 3D. Special mention goes to Goku becoming a Super Saiyan.