The Giants have more wins as a franchise simply because they have been around longer. The New York Giant's first season was in 1925 whereas New England's first season was in 1960. So to be fair, you would need to compare them both starting from the 1960 season. By this comparison, New England has won more games (414) than the NY Giants (390).
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The NY Giants beat the New England Patriots the last time they met in the Super Bowl a few years ago.