Popularity is close. But anything you say regarding Berry's lyrical influence is going to be upsurped by Dylan. And people knocking Dylan's singing doesn't matter because it is only acclaim as a songwriter that is taken into consideration. And as Deany said, Dylan is probably the most acclaimed songwriter of all time unless you count Lennon-McCartney as one songwriter.
his singind does affect him, some of his vocal melodies sound awful, not that they are bad notes per se but the way he sings them, say what you want about dylan expanding berrys template for lyrics, the credit goes to berry, just like alot of guys expanded on the linear drumming steve gadd did when he first used it on 50 ways to leave your lover, but the godfather of that style is steve gadd etc, and dylan is most acclaimed by white aor audiences as the second greatest of all time, not in the circles I hang in ,is he considered the second best.
whatever with all that said
popularity goes to berry,
influence goes to berry (influence is who did it first not who did it better)
and acclaim per se goes to dylan ,
berry still edges out dylan.
Dylan's singing does not affect his songwriting. His vocal melodies were genuinely beautiful; he just wasn't capable of replicating them with his voice. When other artists cover his work, the true genius of his composition comes to light. As for lyrics, Dylan didn't just expand on Berry's template: he kicked down the four metaphorical walls of the box rock lyrics were in and exposed us to the sheer scope of ideas that could be expressed in the genre. Highway 61 Revisited
alone influenced, either directly or indirectly, 90% of all artists that came afterwards. Dylan's influence is continuously felt from the 60's, to the modern day, while Berry's songwriting style (continuous, constant riffs; short and sweet songs; realistic narrative lyrics) isn't as ubiquitous anymore.
Popularity is another thing. I'm thinking you're underestimating "Blowin' in the Wind"'s popularity, but covers of Dylan's work are also very popular ("All Along The Watchtower" for example.) As for acclaim, music critics practically worship Dylan's songwriting. The man has been nominated for a Nobel Prize in Literature numerous times, won an honorary Pulitzer Prize for "lyrics that tapped into the zeitgeist and social consciousness of his time", and is continuously praised by musicians and pundits for his songwriting. His songs, though of course more lyrically oriented, have been praised for their complex melodies as well.
So, a more accurate breakdown:
Influence: Berry, but by smaller than I first thought
Acclaim: Dylan all the way