First of all I have never presented the argument that Bradman isn't the greatest batsman to play the game or is over-rated but to empirical evidence that his numbers are open to scrutiny as much as crtitics of Murali and Sachin in particular that argue that their stats are boosted by playing againts minnows and his comparative average is not that far ahead of his closest comtempoary as their final averages would attest.
The strongest bowling attack of Bradman's era was undoubtably his own especially on the flat, spin friendly tracks that he enjoyed at home, the second best was England by some distance and then the W.I attack. Bradman avaraged an amazing, marvelous 89 againts England and that alone is testament to his standing as the best batsman to play the game. Headley before the war averaged around 78 againts the same opponent if not always the againts the same bowlers. The point that I was making is that outside of England, Bradman played three series againts India (avg 178), South Africa (avg 201) and the W.I (avg 74) and all at home, Headley played his only other series vs Australia in Australia who did a wonderfuul job of scouting him during the tour matches long before it was in vouge and found an initial weakness that he, to his immence credit eliminated by the end of the series. Headley never got to face any of the minnows while Bradman faced all three and as any great batsman would appropriately cashed in. The fact was that based on playing againts comparative opponents their records are not that far apart and the fact that Bradman was playing on the strongest team of his era and in a extremely strong batting side (probably the strongest ever) and Headley was the sole quality batsman of his minnow team and the only obstacle between his side and defeat and he only got to play test matches infrequently (19 matches over 10 years) which would not have helped his consistency.
This comparrison is not to even infer that Headley was the superior to Bradman, but definately not half as good either.
The argument can futher extend to players of subsequent era's who faced tougher batting conditions, regulations and opponents.
It was well known that the Australian pitches between the war were not fast and as such not condusive to pace bowling hence the Australian reliance on spin bowling in their attacks and the rules of the day were very batsman friendly as well. The stumps initially were smaller than they are today and the size was increased because of the great man, the LBW rule was such that the ball had to pitch in line with the stumps to gain a positive decision, so anything pitching outside of the off stump would lead to a not out decision, again a reason why leg and lh spin was the prefered method to take wickets in that era. Both of these rule changes were made to made to assist bowlers and to help even the playing field between bat and ball. Finally regarding the level of competion Bradman, as previously discussed faced only one strong attack, and the only ATG bowlers he would have faced were Tate, Larwood and Verity and Verity apart none of them averaged below 29 vs Australia.
The closest modern rivals of the great man were Sobers, Pollock, G. Chappell, V. Richards, Tendulkar and Lara, they all would have faced more varied conditions, stronger teams, more quality bowlers and tougher regulations. Chappell and Viv in particular proved their worth beyond a shadow of a doubt in WSC taking on the best attacks even assembled and dominated, Tendulkar, Ponting and Lara took on the great attacks of the '90's which included such greats as Donald, Pollock, Wasim, Waqar, Ambrose, Walsh, Mcgrath, Warne, Kumble and Muralitharan and more than held their own. Sobers too took on the great bowlers of his era and added to his work load being for long streaches the main strike bowler and at worse the third seamer for his team, and in both events bowling for extended periods (at times the stop bolwer) that would have had to affect his batting, and this would not have helped againts Davidson, Benaud, Gupte, Trueman, Statham, Mahmood and that memorable innings againts Lillee at his very best.
This is in no way to denigrate the fact that Bradman is the greatest batsman to play the game, but to say that he was twice the batsman of some of the players listed above is something that I cannot endorse and evidence and facts cannot support. Sobers in the 60's ran himself ragged with his schedule and bowling work load playing in every first class league to maximise his imcome, destroying his knees and sholder in the process and adding additional challenges to his scoring. The consistency of Tendulkar has been amazing and the totality of his numbers cannot be ignored, 100 international centuries and playing in the amount of grounds and various conditions is a monumental feat, so is the dominace of a Richards againts the fastest of bowlers and the match winning ability of Lara againts the highest quality of opposition.
Bradman is without question the best to have played this great game who encountered a perfect storm and fully capitalised, twice as good as these gentlemen at their very best, not by any objective measure.