Guitar Hero III: Legends of Rock (Game Only)
Saddly, no. The only game that can really relate to this one on the new gen consoles is Rock Band 4. Guitar Hero Live is another option, but has a different play style than the previous Guitar Hero/Rock Band games.
You can use a regular controller if you wanted to
It does not
This can be played with a regular controller (there's even an achievement for it) but it's quite tricky. I believe Green = L Trigger, Red = L Bumper, Yellow = R Bumper, Blue = R Trigger, and Orange = A button.
Thank you for the question, This is the game only.