Rikidozan's was hands down the most influential man in the history of Japanese pro wrestling. Though I'd argue his popularity has since been eclipsed by Antonio Inoki and his longevity. Like Frank Gotch, Rikidozan was cut down close or at the peak of his career, so he suffers in the longevity category. But like Santo he was primarily big and one era of the world, even though he did see consistent success in Hawaii. While Thesz was an international superstar known all over the world like Gotch.
Drawing power - ultimately it's Thesz. Even though Dozan still has TV rating records that have not, and probably will not ever be surpassed. By anyone.
Consistency - has to be Thesz again. Not only was he chosen to lead the NWA during the 50's and 60's. But he remained a big star and was brought back to be it's flagstaff champion in the 70's during his late forties. No other NWA champion had the honor of representing the NWA through two eras.
Longevity - Again has to be Thesz.
Accolades - Thesz was a world champion of some sorts longer than anyone else in history, and while Dozan did defeat Thesz for a major title on American soil, Dozan returned the favor several times. The point should probably go to Thesz for his sheer longevity.
Charisma - Split here. Both men knew how to talk, act, and present themselves to an audience. Perhaps Dozan did it better. He was able to drive interest in the pro wrestling industry, where others had tried to get the industry booming there in the past but failed for some reason or another. The problem is that Thesz was also greatly revered in Japan. And I think he was the ultimate compliment to Dozan. Along with others like Karl Gotch.
Overall legacy - Again it probably should be Thesz. All things considered.
In ring ability - I've seen more of Thesz than I have Dozan. Dozan worked primarily one style with little variation, while Thesz was able to adapt to the changes in the industry and rework his style to suit the needs of the audience. He could work face or heel, and could implement the "entertainment" style as well as anyone else, while still never abandoning his roots as a scientific wrestler.
This match should be Thesz's. Usually Dozan loses to someone allot worse than him [ala Bret Hart] but not this year.
Vote Thesz.