It may not be the Sonic Adventure 3 you were hoping for. But it's not Sonic the Fighters either.
People considered it to be, despite the fact Sega kept saying it wasn't, the 3rd entry of the Sonic Adventure series do to its deep story that (sega claimed this) and the adventuring through hubs.
Sonic 2006 sold a lot before the negative reception started spreading. Putting sales to a halt. However, a lot of the negative reception was overreactions. But, it was so strong, it was considered a universal fact until the present day.
Sonic 2006 has its share of issues. The story itself was actually not that bad. Very well animated cutscenes, and the fact the game ends itself as fixing itself through time. Which actually has me wondering if they knew they were over hyping the game to the point the negative reception would be heavy
Since this is the 360 version, a lot of things missing or randomly vanishing in the PS3 version, which was released one year later or so, are gone. The problem with Sonic 2006 is it's reliance in many part, although not the whole game, on pixel perfect collision detection. The game is clearly rushed in these aspects and it's a benefit and and issue.
One thing about the PPCD is that it makes sure that your actions and attacks hit the mark. The main issues is that this applies to enemies, to landing on platforms, to trying to run along a wall and end up falling in the pit or lava below.
Sonic randomly has stages called Mach Speed zones, where Sonic goes into Sonic and the Secret rings mode and runs just as fast as he does in the hub world, and your only controlling of him is moving him left or right, or jumping.
The fact is that you have to move ahead of time but also not to soon to avoid objects. Hitting anything will send sonic flying off and in MOST cases you will fly off the level and lose a life.
Another issues is vehicles, they have very odd steering and handling. They seem to zip off when you put to much direction on the analog stick.
The game allows you to play as Sonic, Shadow, and the new Silver the hedgehog. The latter is from the future and has a partner named Blaze. Sonic is the character of Speed, Shadow uses vehicles and trucks with guns now despite being just as fast as Sonic before, and Silver is this psychic guy who can make things float.
Each mode gets increasingly repetitive as you continue through the game. With dull graphics in a lot but not all of the games levels/stages, and hub environments. Which all have a fair amount of glitches.
The game however is playable, and you will most likely make it through all 3 stories to get to the real stage and ending. Despite the repetition and glitches. The game has quite a few areas that are quite fun, and in many areas a very nicely made soundtrack. Especially the old kingdom areas 3 themes.
The game is hard to play, and you should only play it if you like a challenge. People who liked the previous adventure platforming like Sonic game will find things to be a bit different in many areas. Otherwise it is an average game that was overhyped.