It's Pierce and it's not even that close. Pierce is a better offensive player, a better defensive player, a better rebounder, and a better passer. Also, Pierce has the edge on 'intangibles'. Ray's intangibles are very good, Pierce's are all world. Consider the following:
1. Overcoming the stabbing innocent.
2. Facing and overcoming all the adversity from fans that he faced mid-career. He also faced sustained criticism pertaining to the way he comported himself when he played for the olympic team.
3. Willingly subjugating his offensive game in '08 for the benefit of the team.
4. Along with Doc, repairing a rocky relationship w/ Doc in 2k8 (number 3 probably had a lot to do with it). Their relationship went from being rocky to being a strength.
5. Pierce vs. Lebron, game 7 in '08.
6. Arguably the best player vs. Detroit in Easter Conference finals, '08.
7. Outplaying Kobe in '08.
They are both very poised players- although it took both of them awhile to get there. But Pierce is the better leader. He was the captain of the '08 championship team and the players deferred to him in the biggest moments. Even now after the emergence of Rondo as the best player on the team, he is still the one that his teammates look to in the biggest moments. And he usually delivers.
Paul Pierce is one of the most mentally tough basketball players I've ever seen. I think he is one of the most underrated players ever. In my lifetime (I'm in my mid 30's), he's the 2nd best Celtic after Bird.