Would be interested to know where you tend to place Barnes among ATG bowlers?
As with all cricketers there are arguments for and against.
Since Barnes played his last Test in 1914, he was been in the “greatest-of-all time” debate, in England at least, for more than a hundred years. His reputation among English bowlers has comfortably outlasted contemporaries, those who went before, and most who came after. He still has most English Test wickets in Australia, on good pitches against decent batsmen.
The Australians appreciated Barnes earlier than his own countrymen, insisting he was the best English bowler to visit Australia. This view lasted until 1933 when opinion shifted in favour of Larwood.
Once Barnes' reputation became fully established, in 1912, there were few dissenting voices that he was the greatest. Fry had found Lohmann's changes of pace more difficult to handle. Herbie Taylor, the only South African to master Barnes on matting, thought googly bowler Vogler superior. Teammate Faulkner saw plenty of both and disagreed.
Barnes took more wickets in league cricket than anybody, more than 6,000. In all cricket, only the Grace brothers, EM and WG, and the 19th century lob bowler Charles Absolon claimed more.
The arguments against Barnes start with the fact that he was not an automatic pick for England until the age of 36, from when he played four series. After impressing on debut in Australia in 1901, he was chosen for only one of the following fifteen home Tests over a seven year period. He went on one tour, but only after other bowlers had been asked and said no.
Part of the reason was because he opted out of first-class cricket in favour of the better-paid leagues. This didn't impress Lord's who in any case hardly saw him. County cricket was often considered more important than Tests at the time, not least oddly by chairman of selectors Lord Hawke. Wisden in 1908 considered Vogler to be the world's best bowler despite Barnes having just returned from a successful tour of Australia.
Then there was his character. Sulky and bad-tempered, selfish, constantly arguing about money. There were suspicions he didn't always try his hardest, sufficient to lead Cardus to rate him below Richardson and O'Reilly.
Among English bowlers he still probably ranks first. If the acid test is away form, a dozen Englishmen have managed a hundred Test wickets away from home. Barnes averages 17, his nearest rivals 27.
Comparison with men from other countries is harder, but one would expect him to make the Top Ten.