To me there are only two people who could possibly compete for this, John Cena or Shawn Michaels. However my pick for Babyface of the decade would unquestionably be HBK for two reasons, consistency and quality. While both have had very long face runs, HBK's run has been as a face has been longer than Cena's. Granted Michaels' run was broken up by a month long heel turn on Hogan, I think that can be disqualified on account of Hogan's manipulation.
The real factor is the quality. I love Cena. LOVE Cena. the fact that he's as hated by wrestling purists as he is irks me to no end. This guy works his ass off for us and he's booed by fat ass morons in the crowd who think they know what he is and what he stands for.
Whoops... sorry... bit of a rant there.
As much as I respect Cena... HBK takes the cake. The man BROKE HIS BACK in a match and was sidelined for 4 years. He's come back and given us fans something to cheer for every time he steps into a ring. He's the match of the year winner the last 5 years and will no doubt win it again this year with his WM match with the Undertaker. Not only is he a great wrestler, but he continues to get a ridiculous pop every single time he walks through the curtain. Not just from old farts like me that remember everything he did before, but from younger fans that only know his older days with a bad back and a bald head. He somehow still grabs the crowd every single time he enters the ring. To me... that makes a face... and for the last 10 years he has been the best.