Provided you can get past the fact you're playing a Sonic game on a Nintendo console, you'll see that Sega built a better game the second time around.
In terms of levels, music, graphics, and base gameplay, Sonic Adventure 2 was the same game on Dreamcast that it is on the Cube. The graphics are still very colorful and highly polished, and the level design of the Sonic and Shadow stages is still uniquely stylish, but they certainly don't come close to pushing the limitations of Nintendo's bite-sized powerhouse.
Like the graphics, the gameplay is still the same deal on the Cube. You still pick between a "Hero" and "Dark" storyline and lead 3 characters through 16 or so levels of varied gameplay styles. And like the Dreamcast version, the Sonic and Shadow levels are still prime examples of the type of excellent, smooth flowing game design that only years of experience can produce.
However, the fact that the Dreamcast game got ported completely intact isn't exactly a 100% positive thing. While the Sonic and Shadow levels are wonderful all the way through the game, your enjoyment will still be hindered by the inclusion of the tedious scavenger hunts (Knuckles/Rouge) and the half-assed shooting levels (Tails/Eggman). In addition, the pathetic J-pop tunes will make you long for the synthesized classics of the 16 bit era, the storyline will still bore you to tears, and the voice acting still makes Resident Evil look like an Oscar-worthy performance.
The small tweaks made to Sonic Adventure 2: Battle make it the definitive version of the game. In the Dreamcast version, Sonic and Shadow would sometimes appear to perfectly execute a precise jump, but you'd fall to your death anyway due to either a glitch or the hellspawned camera. The camera is still iffy, but this time you seem to be given a much-needed margin of error for precision moves such as landing on rails. The scavenger hunts are also slightly more bearable…for a few moments I almost thought I was having fun. In the original, you had to find your way to the object using only the beeps of your sonar radar. This time around, an exclamation point appears to alert you when the emerald/gate key is right under your nose. Your radar seems more accurate, and makes these levels a little less tedious. There are also a couple of new two-player mini-games, but nothing that warrants a new purchase if you've already invested in the Dreamcast disc. However, it should be noted that the Chao mini-game is a lot more enjoyable now that you transfer them to a Game Boy Advance instead of a VMU. For those who find themselves hooked, it's now a lot easier to raise your creatures on the go.
If you managed to finish the Dreamcast game despite its many obnoxious flaws, there's no need to purchase this update. If you're new to the game, or if you found yourself throwing the controller at the wall from one cheap death too many, Sonic Adventure 2 is a fine place to start your Gamecube platform game collection.
-George