The obvious point is that both men were Italian explorers (Vespucci was from Florence, Columbus from Genoa.) Both men visited the New World on more than one occasion, and both published accounts of their travels, in epistolary form (though Columbus's journal was also published.) While Columbus was more involved with the enterprise of subjugating natives and establishing and exploiting a colony in the name of Spain, Vespucci accompanied voyages as an observer, a navigator, and a cartographer. In fact, he was the head navigator for the Spanish crown at one point in his career. Ultimately, both men did much to capture the European imagination about discoveries in what Vespucci is credited with recognizing as a New World.
One version of the story says that Columbus did not know that he never reached Asia. Vespucci took careful measurements that proved South America was not part of Asia.
I don't know how Vespucci measured longitude, so I don't know how that would have been possible.