We need more options on the Multiple Rings thing. Are you a key contribute on the multiple rings or a bench warmer? Anyway I'm going to just pick HOF player.
HOF= $$$$$ (Barkley, Malone, Stockton,etc) Multiple rings= free meals in the city that you won the ring in (Horry , Fisher, Barry) Easy choice.
The thing is, nowadays everyone's making money. I think a better argument on behalf of HOF is that professional athletes care and neurotically evaluate their own performance as much as their team's success; it's fascinating how well they can recall individual mistakes or sequences of events years later.
I think one of the interesting things about pro ball is that benchwarmers earn their spot like every one else. They practice every day, and if they actually screw up during a game they probably dwell on it and have to live it down a bit more internally and with coaches than starters, who would conversely get it more from the fans and press. So ironically enough the ring might mean more to them.