Wasn't Budokai the Atari games?
Yes that is correct, but NB did revisit the format in some sense with Burst Limit. The problem I had with that one was it felt too stripped down. Plus NB were the ones to release the HD collection of Budokai 1 and 3, so if they wanted to they could produce games in that vein. I honestly think Budokai had a better format than the Tenkaichi set up (But that's just me).
Playstation = The Beast from the East
Sony + Nintendo = WIN! PS3 + PSV + PS4 + Wii U + 3DS