Right...I think Shadow will win because he has Air shoes increasing speed, other moves such as chaos blast increasing power and he can use chaos control, chaos spear, and he can do everything sonic can do + he is the ultimate life form :P Sonic can't top that!
*SPOILER*
*Don't read rest unless you don't want me to spoil game*
Shadow didn't die in Sonic Adventure 2 Battle, Eggman got him back to health but put him in capsule like other shadows like in Sonic heroes (play sonic heroes or Shadow the Hedgehog to find out)