Relative stats in the era would be an actual measuring point if one even wanted to compare them against each other.. the game was played much differently and the quality of the athletes it drew was still in its infancy.. compared to today where players routinely pick football over the other sports.
Couple that with the rules over the years being favored to the offenses and specifically the passing game to open it up. Back then.. there was no 5 yard bump rule, defensive holding, limitations of the pass rushers.. etc.
Example.. pulling probably each QB's best years (to date) in a per game focus in averages across the league:
1966
Comp 15
Att 29
Comp % 51.7
Yards 178
TD 1.3
INT 1.5
YPA 5.6
2011
Comp 20
Att 34
Comp % 58.8
Yards 230
TD 1.5
INT 1.0
YPA 6.3
Personally, I don't think you really can quantify it properly.. to really say one way or another as the game was so different to what is played today. And yearly.. the stats for the top rated passers is becoming even more skewed...
Now on opinion.. I think Rodgers would be more successful if the players were flipped in eras based on their pure talent sets as we know them to be, mostly because I think Rodgers could match Starr's athletic abilities with a better arm. In terms of football IQ.. I think they probably would be comparable.
"The oranges are dry; the apples are mealy; and the papayas... I don't know what's going on with the papayas!"