Zappa is Zappa and he deserves to be there as much as Bob Dylan. Of all the rest, I’d say Zepp edges over everyone else for #2. As for all the rest, well, I think of Neil Young as more of a writer, The Band as sidemen to Dylan, The Animals as one step behind the others. Of the rest I’m giving my vote (again) to Sly and the Family Stone because their Rock/Soul fusion influenced both Funk and Disco.
When this is all over we should have a consolation bracket for all the performers who officially made the RRHOF but fell short on our ballots.
I started to write a longish post, but I’m not actually a huge fan (I do like them just fine), so I’ll just be unusually lazy and link to the legacy section of their wiki 
. They are without a doubt influential and important, partly because they were significant during a seminal period in rock history and influenced a number of Hall of Fame peers. However I would argue that said influence was limited to just a couple of key albums in a few year span. It sorta becomes an exercise is how important seminal albums are for evaluating a career. If ALL Eric Clapton ever did was Derek and the Dominoes’ Layla and Other Assorted Love Songs, considered his masterpiece and enormously influential by most standards, would that be enough for induction?
Personally if the rules were five inductees I’d probably include them, but at three I probably wouldn’t.
That wiki article gives a good outline of how they were regarded by their peers as one of the most influential bands of the time.
I don’t think it’s fair to say the Band were only briefly influential, though. They got famous in 1965 when Dylan hired them to back him up, and broke up in 1978. Like most bands, they did their best-remembered work early, but they were huge for most of that time, with only their last couple of studio albums not selling well. They were only Dylan’s backup band for a few tours in 1965-6 and 1974, both of which produced some of the greatest live recordings of all time.
Along with the Dead and the Allmans, they played for 600,000 people at Watkins Glen in 1973.
Their final concert was filmed by Martin Scorsese and is widely regarded as the best rock film ever. It featured guest appearances from friends and admirers including Bob Dylan, Muddy Waters, Dr. John, Van Morrison, Ringo Starr, Eric Clapton, Ron Wood, Bobby Charles, Neil Diamond, and Paul Butterfield. (I copied and pasted the list from Wikipedia, so you get the links, in case you don’t know who those people are 
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