Compton peaked in the 40s and, by his standards, faded out in the next decade. Sobers' record in the 50s is heavily twisted upwards by the world record score he made. he had a more productive and longer reign as a great batsman in the following decade. but in the 50s, he wasnt a major force with the bat.
so, the answer has to be from one of the three Ws, Hutton, May or Harvey.
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of the six prime candidates walcott and weekes failed in both england and australia. worrell wasn't a great success against and in australia. since england and australia were the most important test playing nations of the decade, this black mark kind of weakens their cases. the same holds true for harvey against england. he wasnt as great a success against the old enemy as he would have liked to be.
peter may had the reputation and the numbers to be called the most influential batter of the era. he was capable of attacking and defending according to the need of the hour. had a long and productive career as the leader and talisman of the team. he was a big match player too. on the negative side, he wasnt a success against pakistan and failed in south africa.
the other candidate, len hutton, failed in that same home series against pakistan in 1954. he was below par in new zealand as well. but he was a great player throughout the decade against everybody else. practically decimated the windies wherever he played them.
all things considered, i would rank them in the order of...
hutton
may
weekes
harvey
walcott
worrell