First of all, I want to clarify that these are loose comparisons and they are not strictly based on musical styles nor follow a unique criterion. Other comparisons and criteria you'd like to contribute are welcome in this thread. THE BEATLES = THE BYRDS When the Byrds appeared on the musical scene in 1965, they were presented as "America's answer to the Beatles". Although the comparison wasn't fair and, indeed, the group from Los Angeles never accepted that label, there are reasons to say that there was a time when they were at the level of the Fab Four. In my opinion, the most creative and innovative period of both bands was 1965-67, when they actually influenced each other. Of course, the Byrds started their career being heavily inspired by the Beatles (apart from Bob Dylan); and it's well known that Roger McGuinn adopted the electric 12-string guitar after watching it in hands of George Harrison in the movie A Hard Day's Night (1964). But then the Byrds defined the folk rock genre with their debut album (Mr. Tambourine Man, 1965), touching the artistic senses of the Beatles and being a major influence for the creation of one of the best albums by the Liverpool's band: Rubber Soul (1965). The Byrds later continued on the innovative path, especially when they recorded "Eight Miles High", song considered as a founder of psychedelia; and the Beatles redoubled the avant-garde bet with "Tomorrow Never Knows", included in the fabulous Revolver (1966). The next year, each band released a new masterpiece: first, the Byrds with the multi-faceted Younger Than Yesterday (1967); and then the Beatles with the famous Sgt. Pepper's Lonely Hearts Club Band (1967). Afterwards, the Byrds were fragmented by internal disputes (McGuinn kept leading different lineups until the end), while the Beatles continued at the top until their separation. But in terms of innovation, I think no other rock/pop band rivaled the Beatles as the Byrds did, at least on American soil. THE ROLLING STONES = THE DOORS Another comparison that isn't new, since the Doors have been seen as an "American reflect" of the Rolling Stones back in the '60s. Even though both bands had blues roots, I understand that the comparison is arguable because the Doors were more focused on psychedelic rock at the beginning, with a very distinctive, keyboard-based sound. But both bands certainly had a very strong figure as lead singer, backed by not less important (though not as visible) musicians. On the artistic aspect, the first two Doors albums (released in 1967) were characterized by dark lyrics and long epic closers, which can be related to previous songs by the Stones such as "Paint It Black" and "Going Home" from Aftermath (1966). Moreover, both groups capitalized a transgressive image, as a contrast to the "good modals" showed by other acts of the time. Coincidentally, in 1967 the Stones and the Doors were invited to play at the Ed Sullivan Show, and they both were asked to change some lyrics using less suggestive words: "let's spend some time together" instead of "let's spend the night together" in the former case; and "girl, we couldn't get much better" instead of "girl, we couldn't get much higher" in the latter case. Reluctantly, Mick Jagger sang the modified part as it was requested; but Jim Morrison did sing (or forgot to change) the original lyric, and the band was never invited again to the show. Eventually, the Doors adopted a definitive blues rock sound in Morrison Hotel (1970) and L.A. Woman (1971), while the Stones returned to their roots and released their four greatest studio albums between 1968 and 1972. THE WHO = JEFFERSON AIRPLANE Perhaps in this case the parallelism is even more forced, but let me explain my point. It is true that the sounds of these great bands were quite different: the Who started as (by nowadays definitions) a proto-punk rock group that derived into hard rock; while Jefferson Airplane started as a folk rock group that derived into acid rock. But the main coincidence I find between them is that both bands shone due to their instrumental virtuosity and were acknowledged because of their live performances. In fact, both groups were key acts in the two great musical festivals of the '60s: Monterey '67 and Woodstock '69. In those events, both the Who and Jefferson Airplane exhibited their technical skills, serving as launching pads to acquire wider fame. THE KINKS = THE BEACH BOYS Once again, here the comparison is not exactly funded on the sound, which certainly was rawer on the side of the Kinks and more refined on the side of the Beach Boys. In this case, the equivalence is related to the idiosyncrasy of both bands. I mean that each group was a faithful reflect of their respective countries: the Kinks showed themes and forms strongly linked to the British culture; and the Beach Boys represented the American culture in a cheerful and natural way. It should be noted, though, that the Kinks presented a more critical attitude, appealing to "social satire"; while the Beach Boys sang from the "American pride", usually referring to their beloved California. Another curious coincidence is the fact that both bands had the special condiment of a "family project", since the Kinks counted with Ray Davies and his brother Dave; and even Ray's wife (Rasa) contributed backing vocals in some songs. The family concept was even stronger in the case of the Beach Boys, with the Wilson brothers (Brian, Carl and Dennis) plus their cousin (Mike Love). THE ZOMBIES = LOVE Two bands that were criminally ignored in their respective home places, but somehow had better luck on the other side of the Atlantic. Both groups managed to create a timeless masterpiece: Forever Changes (1967) by Love; and Odessey And Oracle (1968) by the Zombies. The former album reached the lowest position in the US charts among the first four LPs by Love, peaking at #154; but it had a decent performance in the UK charts, where it reached #24. Meanwhile, the Zombies swan song was not even noticed in UK neither did very well in US (#95); but one track from the album, "Time Of The Season", became a great hit in US, reaching #3 in 1969 (their third and last Top 10 hit in that country) when the band no longer existed. Indeed, the Zombies and Love were soon forgotten after the end of the '60s; but time was good with them and their legacy was restored, especially since the '90s when new generations of music fans were able to appreciate their works.