It wasn't about strength. It was about guile. The Jedi were politically outmaneuvered by Sidious and Anakin's flip-flop is what made it possible as well (and the power of prophecy).
While this will be as hotly debated as tastes great/less filling, Mace had beaten Palpatine. It was Anakin's turn that stopped the good guys from winning there. Yoda was also beating Palpatine, but forgot his physics when it came to compressing energy into smaller and smaller spaces. He ran because he was hurt in the fall, and i'm guessing he lost his saber too.