What turned out to be the most outstanding and important career in popular music was in fact the result of lifelong experimentation, growth and developement. I don't say that anybody here is doing so but it's possible to lose the view for the wholeness of Elvis Presley by "dismissing" a single part of his career. Of course no serious fan would do that. I guess everybody knows how important each decade was to create Elvis Presley. To make a long story short: The question is more or less unanswerable.
Anyway, what this question is all about is personal taste, I guess. While I don't want to miss both, neither the freshness, power, the driving force and initial spark of the 1950ies, nor the greatness and brilliant performance of the "larger than life"-Elvis of the 1970ies it's the 1960ies that probably mean the most to me. They were the corollary and continuation of Elvis Presley's musical concept and the preparation for what followed in the 70ies. His wish to develope as an artist and singer made him the maybe most versatile and professional musician in the history of pop(ular) music.
From rock'n'roll over rhythm & blues, country, soul, gospel, contemporary christian, pop, ballads, Hawaiian, Mexican, even jazz-blues and folk and of course semi-operatic schmaltz Elvis sang it all. Of course he already did some of these styles in the 1950ies, you might say. Of course you're right. But his wish to perfect it not only lead to two wonderful Gospel albums (of one them a Grammy award winner), a Grammy award nominated soundtrack (Blue Hawaii that lost to "West Side Story"(!) only) and two of his best albums ever, "Elvis Is Back!" and "From Elvis In Memphis", both probably more visionary than any others and two of the best rock albums of all time either.
With recording immortal songs like "Are You Lonesome Tonight", "Can't Help Falling In Love", "Surrender", "It's Now Or Never" (to name only a few), less known stuff like "It Hurts Me" and even "Return To Sender", "Bossa Nova Baby" and "Viva Las Vegas", he enhanced the spectrum of rock music in a way excelled probably by The Beatles and Bob Dylan only.
His 1968 NBC-TV-Special - once described by a critic as "music that bleeds" - not only marked the birth of "MTV unplugged" somehow (okay, it was "plugged" in fact but you know what I mean), it's also one if not THE most honest and striking documents in rock music. The way in which Elvis triumphs over the disappointments and lost chances in "Suspicious Minds" or "Any Day Now" finds its counterpart in his return to live performing in 1969 either. I'd say that also his Jan./Feb. 1970 engagement, even the August taping of TTWII are somehow aftershocks of what happened when he finally disburdened from everything that Hollywood meant to him in doing this outstanding sessions in Jan./Feb. 1969.
Like no other decade the 1960ies have it all. Immortal hits, experimenting and developing, they're also about losing it all and winnig it all back in the end. While usually overlooked it's the time of 1966-68 that Elvis probably needed to find himself to some extend. The 1950ies didn't challenge him in a way the 60ies did. And the 70ies made him so great he finally lost the opportunity to accept another challenge. Sadly this was the challenge of his life.