Who deserves to be ranked higher in the all-time lists? I always see Dempsey rated higher by most but I think Tunney is severely underrated. For me it's Tunney. His resume speaks for itself.
I would have said Dempsey and it's not close. Tunney kind of conceded the contest, by retiring in his prime.
Frankly I kind of like Tunney better as career. Dempsey dropped contests to Joe Nobodies which is never a good look. Tunney has the W over Greb whereas Dempsey turned pale at the idea of even facing Greb. Tunney also has the W over Dempsey himself which kind of puts the full stop on the argument. That said, Dempsey was probably better for boxing and has more mystique around him. Stylistically I'm a bit of a fan of Tunney's clever technical style and it's clear through the solidity of his record (no D against Willie Meehan for example) that he was better suited to take on a range of challengers.
Dempsey definitely has a lot more depth. He has five title defenses against Tunney's two. He beat most of the other contenders, before winning the title, while Tunney took a more minimalistic approach.
That's at heavyweight. Probaby, reading the OP again, that is what the question is about. But answering the question "who had the greater career?" the only sensible answer is "Tunney".
P4p list, Tunney should always be higher. Personally I have Tunney in the 12-20 range Dempsey is at very best mid 50s range. Tunney has wins over Greb, Levinsky, Loughran and even 2 wins over Dempsey himself.
Dempsey. He had the longer title reign, more defences. I'd rate him higher on the all-time list. And he was a bigger draw. That makes his the better career by almost any reasonable standard. Tunney was great though and did have a great career in his own right.
It all depends on what you mean bu greater career ... Sociological impact and all time popularity or in the ring accomplishments ? In the ring at heavyweight it's Dempsey .. in the ring overall you have to favor Tunney ... impact on the sport and fame, no question Dempsey ..
At Light Heavyweight, a strong case could be made for Tunney. At Heavyweight, I'd have to go with Dempsey, and it's not close for me.