well define accomplished, because Reem got more titles
Barnett had the UFC belt in 2002 and got it taken for steroids, that was his highest title
Barnett does have the higher profile wins in MMA. The guy is seriously slept-on.
He gave Couture a grappling lesson, had one of the best MMA f!ghts ever w/ Rizzo (avenged this loss too), beat Alexander Emelianenko, submitted Semmy Schilt twice, beat Big NOG in his prime, the only loss he has since 2008 was to Daniel Cormier. Could never figure out Cro Cop in his prime though.
They both have to be near each other in the rankings right now. I would have Barnett #5 and Overeem #6. Would love to see Barnett f!ght Bigfoot next and Overeem f!ght Cigano.