Surprising
Is it because his batting style was slow & boring?
You have to remember, the critics at the time did not have internet and phones, they couldn't just pull up statsguru and look at numbers, so they judged by quality of knocks and memorable performances. Barrington made heaps of runs but most of his runs were on pitches specifically made for draws, Cowdrey has the more memorable performances in Ashes test.
Cowdrey, when 22 years old, made a 100 in Melbourne so good that Bill O Reilly thought it was the best inning he ever saw, he made 102 runs against Ray Lindwall/Keith Miller/William Johnston/Richie Benaud/Ronald Archer on an impossible pitch where England were out for 191. Cowdrey made 102, Rest made 80 runs for 9 wickets. This resulted in an English victory
in 1958-59, everything went wrong for England in Australia but it was Cowdrey who made a hundred against the Australians to allow England to save a game and not lose 0-5.
or in 1962-1963, In Trueman's game at Melbourne, Cowdrey and Dexter made 113 and 93 together coming in at 2-19 against a very strong Australian bowling to take England to 300+ and then both came and made 50s to chase down 240 on the final day, resulting in an English win.
meaning that Cowdrey has two match winning performances in Australian Ashes, and one match saving, the first being maybe top 10 hundreds ever. This is what people remembered mainly.
He had many such performances, he made 154 at Lords against a good Windies bowling coming in at 3-34 to win a game, he had a classic twin hundred performance against Wes Hall on a very fast pitch etc.
Though, that being said, Statistically they are not close at all, during the duration of Barrington's career, from 1959~ to 1968~, During Barrington's career
Barrington: 59.76
Cowdrey: 50.48
Dexter: 50.51
away from home
Barrington: 69.18
Cowdrey: 62.07
Dexter: 58.02
at home
Barrington: 52.30
Cowdrey: 42.50
Dexter: 43.62