I think the Beat poets saw themselves as a separate movement with its own identity. When I think of the Beats, I think of individuality. They were interested in art for art’s sake, and had a unique approach to poetry that was very personal and did not copy other styles. You can read more about the Beat Generation here:
The big difference has to be the drug use and experimentation with sexualization. Transcendentalists may have believed in one's ability to obtain a higher consciousness, but they also believed in something greater than themselves, whether that was God or the Universe. Transcendentalists didn't believe in self-destructive behaviors as a way to discover greatness, the Beats, at different points in their own lives, in fact, did. Eventually, the Beats leaned towards believing in the universe through Buddism or Zen or Hinduism. The Beats' exploration into the Asian cultures and religions happened after they couldn't find much through drug use. I can't imagine Whitman or Emerson smoking weed or experimenting with women or drugs. :)
Even if the Beats might have said they did not wish to be seen as Transcendentalists, they have quite a bit in common with the older literary movement. An influence from eastern religions, specifically Hinduism, is clear in the work of Emerson, Whitman, Ginsberg and Kerouac.
Also, Whitman's influence on the style of both Ginsberg and Kerouac is definite. The use of rhapsody and lists in the construction of the poetic and narrative voice is characteristic of all three of these writers.
Have you read somewhere that the Beats sought to distance themselves from the Transcendentalists? I have only seen quotes that have the Beat writers praising the work of people who came before them...