My reasoning (flawed as it may be):
I love Jimi Hendrix, but he would have ran out of ideas and crawled up his own ass by 1982. He would have been a mentor of sorts to Prince though.
Jim Morrison was well on his way to becoming a bloated and pretentious joke, but he died before it came to fruition. Everybody nowadays prefers the "Light My Fire/Lizard King" Morrison over the "L.A. Woman/Beardy Alcoholic" Morrison.
If the shotgun hadn't killed Kurt Cobain, it would have been the needle. Had he survived his addiction and gotten sober, the impact would have lessened significantly and Eddie Vedder would be more influencial.
After spending the second half of the 1970's and all of the 1980's in semi-retirement, Janis Joplin would have made a glorious comeback in 1994. Her headling all Lilith Fair tours would top Lollapalloza in dollars and cultural impact.
The winner: Janis Joplin!