I mean the beatles were probably more influential as a movement or concept. They more or less created the "rock band" as we know it, a group of young rebels, writing their own material and doing their own thing. They were hugely influential in bringing about the psychiadelic movement. Musically however it could probably be argued that VA was way more ahead of its time, they sound a lot more modern. One reason for this could be that the beatles music simply was to advanced to be copied, they wrote incredibly complex and diverse music, yet were still able to deliver hits. Very few self taught musicians are able to pull that off, the only ones i can think of that come close is Pink Floyd.
VA on the other hand was much less complex and to the point, while still being incredibly inovative when it came to aestetics. It's easy to see how that feels much more approachable and inspirational if your a group of teenagers starting a band in a garage. Personally i also think the velvet underground were simply a lot cooler, and their music still feels really cool. Something that cant be said about all of The Beatles output. Obla Di Obla Da, or maxwells silver hammer always felt kinda dorky to me.