Comparing Shermans to Tigers is like comparing oranges to apples.
The Sherman and the Tiger are not of the same class.
They were designed for different roles, the Sherman being a mobile multi-purpose platform to support the infantry while the Tiger as a “breakthrough” tank designed to rule open country tank to tank engagements.
Shermans are not even supposed to deal with Tigers. US armor philosophy prescribed that the tank destroyers are the ones who should deal with them while the Shermans should support infantry operations. But more often than not, Shermans found themselves confronting Tigers and Panthers. Not really on purpose but rather (IMHO) by chance or lack of choice (when tank destroyers are not available.)
We cannot really or ABSOLUTELY say that the Sherman won over the Tiger. Or the allies won the war because of the Sherman. Or Germany lost the war because of the Tiger. The Sherman was only one of the major factors that contributed to the success of the allies.
We can compare the Sherman and the Tiger for the sake of comparison. But we have to bear in mind that these tanks were not of the same class and were not designed for exactly the same purpose.