Now this is an Interesting thread.
So, I personally believe Hobbs was further ahead of his peers than Barnes, the names that seem close to Hobbs on the sheets are Warren Bardsley, Victor Trumper and Aubrey Faulkner, as you'd notice, all South African and Australian Batsmen. The 1910-11 Australia vs South Africa series is an outlier to the golden era as it was by far the highest scoring series of the Golden Era. Even by modern standards the series is above average in scoring, let alone Golden Era standards.
While Aubrey Faulkner certainly deserves credit for what he achieved against Australia, one must understand that Australia had been pretty hard good batting wickets since 1890s, and the main South African bowlers, in Aubrey Faulkner and Bert Vogler, both were complete failiures that series as Faulkner had neglected his bowling to focus on his batting and Vogler was more or less finished and had his alcohol issues on top.
All these factors combining, South African bowling failed badly, thus Trumper/Bardsley/Hill easily picked them apart in their home conditions, their runs were easier than pretty much any other runs made in the era, therefore I believe a fairer comparison to Hobbs would be removing that series, and in that context from 1907 to the second war..
Jack Hobbs: 57.64
Victor Trumper: 30.66
Warren Bardsley: 38.20
Clem Hill: 31.70
Aubrey Faulkner: 35.66/46.70 [with Australia tour]
Wilfred Rhodes: 34.21
Frank Woolley: 32.31
Though Faulkner does deserve credit for what he achieved, considering Australia likely played a full strength attack against Faulkner at the very least. The Point stands, outside of the series where Australian Batsmen certainly had an easier time than everyone else, Hobbs was absurdly ahead of anyone in the second part of the Golden Age.
Just for record, if one wants to use Aubrey Faulkner as a point of argument, Hobbs averages 58 to Aubrey's 40 in the pre war era, assuming we're rightfully including the debut serieses for both, if not, Hobbs would go over 60 while Aubrey would be in mid 40s...while Faulkner batted in the middle order and Hobbs opened.
Now regarding Sydney Barnes, Standing out like that in a bowling dominant era while being a bowler is absurd, for example, the 2000s was a batting era and someone like Ponting ended up averaging less than someone like Younis Khan even though we all know the prior was far beyond the latter, that is a real risk of happening with someone like Barnes but the way he dominated the bowling era is absurd, on English wet wickets and South African matting wickets he was practically unplayable, in those two countries he has 112 @ 12.3 with 16 5fers and 6 10fers in 14 games, he was also dominant on Australian batting wickets, it's been around 110 years since Barnes played his last test Cricket match and he is still tied with Richard Hadlee on most wickets in Australia of a touring bowler, he has 1 less wicket than Ambrose in Australia while Ambrose has bowled in 3 more innings.
6 WPM in Australia, 22 average, 8 5fers in just 25 innings, many match winning spells and there was nothing wrong with those wickets to bat on really, not uber flat like the 2000s and 2010s counterparts but not really extremely difficult like the current wickets or the 1950s ones and he was undisputedly the best bowler of the generation and was viewed as the best bowler in England and South Africa until those who saw him died and the only debate in Australia was Bill O Reilly. The West Indies saw Barnes in 1928-29 and they also deemed him the best they saw whole season in his complete old age, better than Larwood, Voce and Bowes.
All in all, who is the better Cricketer? that's Sir Jack Hobbs, He came back after the war and murdered the likes of Ted McDonald, Learie Constantine, Jack Gregory, Clarence Grimmett, Manny Martindale etc and was the dominant English batter for another decade, insane longevity and the feat of being one of the best players in International Cricket in your 40s after so many health issues is genuinely unprecedented in the hundreds of years of history of this great sport. Who was the greater Cricketer? once again, Jack Hobbs, because under him people like Hammond and Sutcliffe emerged and he was England's greatest Batsmen for two decades, He was so brilliant that until the 1960s or 70s, he was viewed as close to the Don himself.
but for the context of this thread, we're to limit ourselves to pre-1914 content, considering even though I believe Barnes could've but he did not return to dominate World Cricket after the first war, and therefore the whole discussion would be Pre-WWI Hobbs vs Pre-WWI Barnes and I think that is extremely close, Hobbs by far the best Batsmen but Barnes was also by far the best bowler even if, by a lesser margin.
One thing I would take into account is relative longevity, Hobbs played from 1908 to Pre-World War I but Barnes started his career in 1901, He didn't play inbetween but that is less to do with quality than to do with his behaviour. Fact of the matter is, he debuted in 1901, in his first two games his figures were –> 5/65, 1/74, 6/42, 7/121, and that was in Australia, he then bowled in 1902 in England and got 6/49 first attempt as well. I've no doubt that had he bowled from 1903-1906, he would've been extremely successful as well.
All in all, very close one, Barnes likely superior and the bigger match winner in England and South Africa, Hobbs likely the better one in Australia, Hobbs more of an outlier but Barnes was likely quality for longer before the first war, Hobbs obviously pulls well ahead of Barnes with his Interwar period achievements. But If the careers had ended at the first war? Hm, Maybe Barnes by the smallest gap imaginable, might change to Hobbs on another day however.
anyway, apologies if I talked too much, simply found the topic interesting.