The answer depends on the definition of "success," but we would probably say that Katherina has the most successful marriage. Both she and Petruchio are unorthodox characters who behave in unorthodox ways. By finally slipping into the "ideal wife" model, Katherina gives Petruchio little choice but to moderate his own eccentricity and live up to the "ideal husband" model of the time, which was not quite as tyrannical as some modern students might think (cf. Healey's article referenced below). Katherina's submission is a judo move, in which the strength of Petruchio's assault on her is turned against him. Now the eye of society will be directed towards him to see if he measures up.
Bianca, on the other hand, as shown by her behavior, has taken the superficially more dominant but actually more vulnerable role of the nagging, defiant wife. She can dominate her husband, but in an unsubtle way and one that is strongly depreciated by society. Thus, she is at first sight in a more empowered position, but in the long term she will attract much more hostility from society than Katherina will.
So, to sum up, in the short term it might seem that Bianca has made the better marriage (in the sense that she has more control and agency over her own life), but in the long term Katherina, if she continues to leverage social expectations in her favor, has a better chance of getting her way with the minimum of effort.