So I have gone back and forth on this one and I am ready to present my case...
Drawing power - As far as a drawing card goes Backlund was far bigger. Rikidozan achieved unparalleled feats such as drawing television ratings of 87.0 against Lou Thesz and later 67.0 against Destroyer. Compared to the US Japan has always had a history of inflated ticket prices, and even though Rikidozan himself was a huge draw, he just can't touch Backlund's longevity. As far as marketability went Rikidozan was easily superior. He was the poster boy for all things Japanese wrestling in the 50's and early 60's.
Longevity - Rikidozan's career only lasted 12 years, and he was cut down in his prime by a Yakuza gangster. Backlund had the second longest WWE championship reign after Bruno Sammartino. And like Bruno, Bob was an international known superstar that travelled everywhere, defended everywhere, and drew everywhere. By the end of the 5 year run fans may have been beginning to tire of him, but that didn't stop Backlund from reinventing himself and winning the world title in another era. Point Backlund.
Consistency - Rikidozan was practically undefeated his whole career. Very few men pinned Rikidozan. Even outside of Japan. Most of which did were foreigners. It was exceedingly rare for Dozan to lose to a fellow Japanese. One of his controversies was the shoot match where he kicked the ever loving shit out of Masahiko Kimura, he himself had been undefeated for a decade. And part of that stemmed from his JWA beneficiaries wanting to make Kimura into a top star, but Dozan was not willing to share the spotlight. Backlund did go [WWE kayfabe] undefeated for 5 years, but then lost in 8 seconds to Diesel of all people after choking the fuck out of Bret Hart. Like that makes any sense. Ultimately I'd say Rikidozan has the edge.
Charisma - Rikidozan embodied it, but so did Bob Backlund. Most are quick to write Backlund off as a boring champion, but he wasn't. Far from it actually. And his later run as Mr. Backlund showed how much versatility the man truly had. Rikidozan worked primarily as a super face in Japan and as a heel in the States, but there were times where he could and did work face in the States. His WWA world title match in 1962 against Fred Blassie in California is an example. I think Backlund has the edge here. As a performer he seemed much more natural and organic. If Dozan worked face in the States it's because his opponent was a huge heel. Otherwise he rode the train of nationalism like several others before and after him did. Like Santo in Mexico and Hogan in the 80's.
Accolades - On paper Backlund has the advantage. One of the top promotions in the world at the time entrusted him with their strap for an extended amount of time and he excelled. As the primary star power for the JWA, Rikidozan pushed himself as world champion, but the belt did not hold much prestige. It wasn't until Dozan defeated Thesz for the NWA International Heavyweight Championship [which itself was just a prop Thesz created so that he could wrestle in Japan and avoid the politics of the NWA] that Dozan finally held a credible title. Where Dozan made most of his money is through tournaments. The predecessor to the modern G1-Climax, Dozan's World League was very popular. Dozan won 5 of them, the reason he didn't win a 6th was because he was dead by that point. I think in the interest of success I give a slight edge to Dozan here. These tournaments did help start a tradition that is still enjoyed by Japanese wrestling fans today. But Backlund's historic run cannot be undersold.
Overall influence - Rikidozan laid the foundation for what is now modern Japanese wrestling. Whether or not his two greatest students Antonio Inoki and Giant Baba surpassed him is another debate entirely, but Rikidozan remains an important historical figure and national hero to this day, even if his later career was marred in controversy. Not wanting to put over domestic talent and making poor business decisions that would ultimately cost him his life. Backlund carried the WWE through most of the 70's and was the bridge between Bruno and Hogan. He was the golden boy that fans loved. And the recreation of his gimmick in the 90's afforded him even more respect. Tough call.
In ring ability - Most subjective category. According to Lou Thesz, Dozan was a capable grappler but not top class. Backlund on the other hand was. He was a former NCAA champion. Both of these guys were around the same size and possessed tremendous strength. Watching some old matches between Hogan and Backlund, Bob handled the 300 pound Hogan like a child at times, which is seriously impressive. Dozan had tremendous balance from his career as a sumo and utilized allot of those techniques.
Since one of these guys has to face the [very likely] Brock Smash next round, I feel more compelled to vote for Backlund because he's more known to the forums and his style and accomplishments mesh better with Brock's. From a kayfabe perspective it's Dozan's win. He rarely ever lost. And while Backlund did spend several years being largely unbeatable, his consistency is no where near Dozan's.