Shadow is much more powerful than Sonic and in a fair fight he usually wins. In Sonic Adventure 2 Shadow canonically defeated Sonic, only after his victory Last Story can be started. If Sonic wins, he destroys the Eclipse canon, but as we see in the Last story the canon is undamaged and working. 

Sonic Battle is non canon and Sonic there managed to beat Shadow only because Shadow was injured.

Not to mention Shadow has limiter rings that restrain his full power.