I think it was a combination of the two. Vietnam actually lays at Eisenhower's feet. My dad had a friend (whom I also knew) who was an ‘advisor’ from ’58–60. You might even argue that Truman committed the original sin, if you will, by aiding the French in 1948.
But, to your question, they both bare responsibility. Johnson, for the lie that put troops there and Old Tanned Rested and Ready for escalating it and bombing Laos and Cambodia in doing so. Don’t forget who was in both Cabinet’s, either. The war criminal himself, Hank the K.