No band won the 1993 MTV Video Music Award for Video of the Year with “In the End,” because that song was released by Linkin Park in 2000.
The question combines two different MTV-era facts. Linkin Park’s “In the End” became a major early-2000s hit, but it was not eligible for the 1993 awards. The 1993 Video of the Year award went to Pearl Jam for “Jeremy.”
“In the End” appeared on Linkin Park’s debut album Hybrid Theory, released in 2000, and its music video became an important part of the group’s MTV-era visibility. The band’s award history therefore belongs to a later period than Nirvana, Pearl Jam, and other leading early-1990s MTV acts.
This is a deliberate factual correction rather than a conventional answer: the premise has no valid winner. The year and song do not match.