Firstly, I should point out that in the world of rock'n'roll criticism, etc, Elvis isn't necessarily always seen as tacky/trashy: there are 11 Elvis songs in Rolling Stone's list of the 500 Greatest Songs (including 'Hound Dog' at #19, 'Heartbreak Hotel' at #45, 'Jailhouse Rock' at #67, 'Mystery Train' at #77, and 'Suspicious Minds' at #91.) You'll note that almost everything on the list is from Elvis's imperial phase (1955-1957) with the notable exception of 'Suspicious Minds' (which is from the late sixties album From Elvis In Memphis). Elvis is still given his due for his pioneering rock'n'roll success, and a good Elvis best-of is still one of the records you'd suggest to someone who wanted to understand 1950s rock'n'roll.

It's what came after 1957 that's the problem in terms of Elvis's public image. Elvis famously was drafted into the US Army, and was stationed in Germany, leaving him unable to record and promote music for a good period of time. Elvis's comeback record Elvis Is Back in 1960 generally is seen to be a minor classic (if not quite at the level of his imperial phase.) It's what comes after that which does harm to his public reputation: he starred in 27 formulaic Hollywood musicals in the 1960s, none of which has an IMDB rating above 7.0, and where there's a notable decrease in the average score over time. Additionally, most of his 1960s albums were soundtracks to these films, and almost none of those 1960s soundtrack albums were critically acclaimed. Stephen Thomas Erlewine at Allmusic argues that the Harum Scarum soundtrack was where Elvis started hitting rock bottom, and that was in 1965. And while Elvis hit musical rock bottom in 1965, younger acts took the rock'n'roll sounds he had previously made, once upon a time, into an explicitly countercultural place that Elvis could not hope to follow.

Elvis's soundtrack albums were severely limited in a variety of ways; firstly, for contractual reasons, Elvis's soundtracks, especially as the 1960s progressed, tended to avoid using songs by the rock'n'roll likes of Lieber and Stoller, or Otis Blackwell, because of a deal that Elvis's people had with the publishers Hill & Range where Elvis would get a cut of the songwriting royalties if he recorded a Hill & Range song. Over the 1960s, the quality of Hill & Range songs nosedived, and by 1968, Elvis's career was clearly going south. Secondly, there's a sense that Elvis was just pumping out so much material that most of it was likely to be forgettable. Thirdly, Elvis as a Hollywood star (who perhaps more than most lived in a bubble) was insulated from the musical foment occurring in the 1960s, and his records were produced by Colonel Parker, a man who was born in 1909 and who was not exactly hip-and-with-it.

As a result, he recorded the Comeback TV special where he, you know, played the songs that had made him famous in a rock'n'roll style - something he hadn't done quite some time, to the frustration of many of his old fans. The next year he released the album From Elvis In Memphis which was widely seen as a return to form; From Elvis In Memphis was produced by a more contemporary producer, Chips Moman, rather than Elvis's manager Colonel Parker, and included 'In The Ghetto', along with covers of songs by Philly soul magnates Gamble & Huff, Burt Bacharach, and Hank Snow. From the same sessions soon came 'Suspicious Minds'.

However, Elvis's late 1960s artistic renaissance was shortlived, as he began a longrunning residency at Las Vegas in July 1969. Las Vegas, in terms of pop culture, does have a particularly tacky/trashy aesthetic attached - 'what happens in Vegas stays in Vegas' and all that - and for a younger generation who were less interested in the older generation of crooners, Elvis began to symbolise 'going Vegas', especially as he put on weight, wrestled with mental health problems, and musically retreated into kitsch Vegas professionalism. It's this 1970s Elvis which, more or less, is the public image of Elvis as trashy/tacky, probably notably codified in Andy Kaufman's prominent comedic Elvis impersonation (e.g., here on Johnny Carson in 1977).

As to why Elvis has ended up tacky/trashy and The Beatles haven't - the Beatles have ended up having a 'have it both ways' space in pop culture where because their body of work occurred over a limited period of time, they ended up going out on top; if the Beatles had stayed together and released an album in 1976, it likely would have been received just as poorly as that Elvis album in 1965; instead it was just Ringo and Wings albums that were received poorly. The Beatles also have the advantage of being the favourite band of the baby boomer generation, which still exerts an outsize pull on pop culture and especially on the iconography of rock'n'roll; while the baby boomers give Elvis his due (see his presence in the top 500 poll by Rolling Stone, the epitome of the baby boomer rock magazine), he is ultimately the icon of a generation that's slightly older than the baby boomers.

And, well, I think I'd prefer to have Elvis's kitschy public reputation than the public reputation of Michael Jackson, which often is focused on some quite bizarre behaviour and some troubling accusations of untoward behaviour around children.