Who beat better opposition Sonny Liston or Jack Dempsey

Nobody else does. In terms of resume (without including another defeat) Cleveland was already 0-1 against current rated guys fighting Liston.

Against actual rated fighters when "he fought them" Williams improved to 1-8-1 by the time he retired.

This is not a major player.

 

Yes, but Johansson had only one victory over a currently rated opponent when he fought Patterson according to The Boxing Register.

Johansson had no wins over a rated opponent when he fought Machen and still he KO'd Machen in one round.

Also, I am not so certain your numbers are accurate. I think Billy Daniels alone was rated in both fights with Williams. I think Miteff was rated also.

And quite a few of those defeats came when Williams was old.

From 1956 to 1966, Williams lost only via a split decision to Terrell, who beat Zora Folley much more decisively in his next fight,

and to Liston twice.

That really isn't a bad downside. Brennan, for example, was losing or fighting draws, with second rate fighters right through his career.

Bottom line--I think you have a fair point, but you're carrying it way too far. I think SuzieQ takes his fair point too far in the other direction, making Williams basically the terror of the heavyweights. I see it somewhere in the middle--a good fighter who never really flopped (unless one considers losing badly to the very best a flop) but whose resume is thin for a top man.

I think his ratings, rising to number four, are a pretty good balance to the competing views and about where I would place Williams.

 

Just on Cleveland Williams--I bumped a thread posted by Senor Pepe on the Liston-King fight of 1960 which concludes with comment about Liston and Willams.

"After this bout Texas Boxing Enterprises offered Sonny Liston a boxing contract to go to Texas to fight #3 heavyweight--Cleveland Williams in Houston for a bout set for March 21, 1960."

Where did this #3 heavyweight come from?

Is this the NBA ratings?

I don't know all the facts, but the New York based Ring Magazine was closely tied to the New York boxing scene, and the NBC Friday Night Fights usually from Madison Square Garden.

The NBA seems to have been tied to the ABC Wednesday Night Fights, generally from the Chicago Stadium or Midwestern or Miami venues.

To make a long story short, Williams seems to have been rated earlier by the NBA. He broke into the Ring ratings when he began fighting on the then Saturday Night Fights, centered at Madison Square Garden and the New York boxing scene.