Looking selectively at aspects of a players' career is often a false argument. It is easy to understand how looking through rose coloured glasses can distort the overall performances of any ATG. Unless we look at the other side of the coin, we never get the complete picture, so both sides need to be considered, In the case of Gavaskar, there is no doubting he deserves to be regarded in the top echelon of all-time openers.
However, looking at performances over various aspects of a career can be misleading. True, Gavaskar averaged over 70 in 13 Tests played in the West Indies and 65.45 in 27 Tests against that opponent. But if we are going to look at specific countries, his record in England (41.14 in 16 Tests) and overall against that country (38.20 in 38 Tests) is far from ATG level.
Hutton's war-time accident has been mentioned here. While he successfully modified his style, he was placed under extreme pressure against The Invincibles when Bradman ordered his quicks (Lindwall, Miller and Davidson) to attack him with short pitched deliveries knowing Hutton's pre-war hook shot was no longer a weapon.
Given that Hutton's pre WWII Test batting average was 67.25 , I have often wondered (as with Bradman) what his career stats would have looked like without the lost war years.
Having seen Hutton, but not having had the pleasure of seeing Hobbs, I can't separate the two. Gavaskar has been thrown into the discussion, and deservedly so, but having watched him, I can't rank him above Hutton.