The 2001 SE, hands down.
It gives a greater sense of how the show was put together, and gives greater credit to the musicians and singers who backed Elvis.
The original 1970 film lacked cohesion, and too much time was wasted with that embarrassing footage of the UK fans at the Luxemburg convention, especially the Mystery Train sequence, where the Elvis Costello lookalike merges with Elvis on stage during the song. Just awful!
And in the original, after Elvis came on stage, he was interrupted by fan comments after just one song, and periodically thereafter (although I'm prepared to allow the comments from that editor of Tiger Beat magazine, because she was so cute! )
What I like about the SE, is that once Elvis is on stage ... that's it until the closing credits! The main criticism, though, is that it actually runs shorter than the original. But it's a better film all round.
Having said that, it's good to have both versions out now on DVD.