There are places I remember

The Beatles - Rubber Soul - 1965

I tend to consider this album and Revolver (which I'm going to devout a whole post to) as two sides of a coin, the coin being the transition between the earlier, simpler Beatles, and the latter, more "out there" ones. It was the one that started having a slightly more "experimental" sound to it, with the first, almost shy, appearances of more unusual instruments, like the sitar, as well as incorporation of more European influences. The lyrics were evolving too, moving away from the typical "boy loves girl" topics to more complex takes on couples' relations, as well as some more existential lyrics. Still, I see this as part of their earlier albums, and its a damn good one at that.

• "Nowhere Man" is, probably, the first song to really deal with deeper topics, such as what's the meaning of life, and where does one's life go.
• One of the two songs written by George, "Think for Yourself", is one of the earliest cases in which a Beatles song allowed for some ambiguity in the interpretation for the lyrics. At first sight, it can be interpreted as a post break-up song. But we can't ignore the fact that it can as easily be seen as a song that has a more universal reach, telling everybody to think for themselves. Considering that it was written at the time George (as well as John) had started their experimentation with drugs, the latter interpretation seems like a very valid one.
• Apparently, "Michelle" started out like a half-joke song, in which Paul would sing mock-French "words", just to laugh at some art student at a party, who would sing in French. The song later evolved into its final form, which sounds a lot like French songs at the time.
• Incidentally, "Michelle" won the Beatles a Grammy in 1967, beating classics such as "Strangers in the Night" and "Born Free." As much as I think that it was John's more daring style of writing and singing that earned them respect beyond the "boy-band" trope, I believe it was Paul's compositions and melodious voice that gave them a more universal appeal. 
• Whenever I see or hear something that from our 2018 politically correct world seems out of place, I always try to put things into context (and for the most part I end up concluding that people were less silly back then). Still, I have to admit I winced when I heard the beginning of "Run for your Life": "It rather see you dead. little girl / than to be with another man."
• In this album, we also have the first "reminiscence" Lennon's song, "In my Life". It's an old favourite of mine. The piano solo in the middle is an absolute classic.

Things are different today

The Rolling Stones - Aftermath - 1966

And yes, it was high time we got to the Rolling Stones, and I am a bit embarrassed to realise that I don't have anything prior to this one.
Hadn't heard this one in a good while and, in retrospect, it seems to me much more juvenile, at least with respect to the lyrics, than the Beatles were. The music does feel a bit more evolved, and I enjoy the more bluesy/rock sound, the guitar riffs and Mick Jagger's voice and style of singing. It does feel like a very uneven album, with a lot of filler there, but the best tracks are really cool.
But as far as lyrics goes, this is almost as silly as punk. It's way too much the story of a bunch of annoying kids trying to get laid (and getting angry because they can't). Not that I think it was the case for them, but I can see a lot of frustrated kids liking them back them.

• This was the first album to include an 11 minute song. Not just by them, by anybody, at least in pop / rock music. It's "Goin' Home", and it's pretty much a jam with Jagger repeating different variations on phrases on the lyrics. It's a good tune, I just wished the long time had allowed for more musicianship.
• The opening track, "Mother's Little Helper"deals with the increase in use of prescription pills by housewives, and it's by far, the song with the best lyrics in the album.
• Yes, yes, I know, "Under my Thumb" is sexist and stupid. It's also such an awesome song, that it doesn't really matter. 
• Listening to some of these songs, like "It's not Easy", or "Dontcha Bother me", it surprises me to realise how consistent they remained musically for the most part.

Nunca, Nunca

Los Shakers - For You - 1966

And, of course, the Beatlemania was not restricted to Europe and the US. It got to the Rio de la Plata shores in the form of a band called Los Shakers, from Uruguay. The band started after brothers Hugo and Osvaldo Fattoruso  watched A Hard Day's Night, and they cloned the Beatles as much as they could. Apparently they were hugely successful in Argentina as in their own country. This album is the only one I know by them (other than that there was a previous single, "Break it all", which is quite well known), and it does have some interesting aspects, and the musicianship is surprisingly good. Both brothers came to be very well respected musicians, who played with international artists (Osvaldo died in 2012). But they seem a bit too much of a Beatles copy to me, to be honest. A fun one, though.

• Listening to this one in the context of Rubber Soul doesn't help either. There's a song in French, "Reviens ma Cherie", whose guitar work sounds a lot like "Norwegian Wood". 
• In the same vein, the last song is full of psychedelic sounds, tape loops, dubbings, in the style of "Tomorrow Never Knows", from Revolver (this one was released just a couple of months after the Beatles' one).

Random thoughts

• Can anybody explain what on earth was the deal with UK vs. US releases of albums back then? Still today there may be 1 extra (or different) song between two different releases, but back then it was completely insane! Different songs, different album names, was it so hard to get it right?