I agree, in fact, I prefer this version over the studio version.
In comparison the studio version is well polished, in that Elvis (a young man who had possibly not yet felt the pain of being truly heartbroken) and the band had many takes to nail this track down.
Whereas the live version is sung by a man with more life experience, currently undergoing his own painful separation. On that April evening he only had one shot at it......and he delivered, an impassioned, inspired performance.
I love the line, "honey, you lied when you said you loved me"