I am going to attempt to compare the evolution of both bands through their albums side by side comparisons........I think it will be admitted that there are a lot of interesting congruencies.
The Beatles - Please Please Me (1963)
Pink Floyd - Piper At The Gates of Dawn (1967)
Both very strong debuts. I personally find myself more interested in Piper than Please Please Me.
The Beatles - With The Beatles (1963)
Pink Floyd - A Saucerful Of Secrets (1968)
Both albums are weaker than the debuts, but involve a little more studio experimentation. Vote goes to the Beatles here
The Beatles - A Hard Day's Night (1964)
Pink Floyd - More (1969)
Both are the soundtrack to a movie. The Beatles album is clearly better here. Very solid!
The Beatles - Beatles For Sale (1964)
Pink Floyd - Ummagumma (1969)
Not much to talk about as being in common here, but I think that both albums show a distinctly more serious side to both bands. My vote would be for The Beatles here
The Beatles - Help! (1965)
Pink Floyd - Atom Heart Mother (1970)
Help! is the Beatles second soundtrack and while it's not as strong an album as A Hard Day's night it does yield the title track and the Beatles' most famous song, Yesterday. Atom Heart Mother is very solid masterwork as well. I'll give the vote to the Floyd here.
The Beatles -Past Masters Vol. 1 (1988 [1962-1965])
Pink Floyd - Obscured by Clouds (1972)
I'm using a little liberty to skip over Meddle for a second because I think Pink Floyd was working on this album first and ALSO it is not nearly as interesting. Past Masters is a collection of all the singles which did not appear on LPs. It's not fair to call Past Masters an "album" per say, but I will still grant The Beatles a superior status here.
The Beatles - Rubber Soul (1965)
Pink Floyd - Meddle (1971)
This is where things get interesting. This is where the Beatles began creating serious art, and this is where Floyd began really crystalizing their vision. I have to give the Beatles the award here.
The Beatles - Revolver (1966)
Pink Floyd - Dark Side Of The Moon (1973)
OK, this is a tough call. Both Revolver and DSOTM can be seen as part two of their previous album, I have to give the award to Pink Floyd, but this was SO damn tough.
The Beatles - Sgt Pepper's Lonely Hearts Club Band (1967)
Pink Floyd - Wish You Were Here (1975)
Both albums are often thought of as the ultimate studio masterwork of both bands, while both of the previous albums are considered a bit more influential. I have to say Pepper wins here, even a devoted Floyd-ster would have to see that.
The Beatles - Magical Mystery Tour (1967)
Pink Floyd - Animals (1977)
Amazing similarities between the mention of animals. Beatles win on the strength of superior songwriting.
The Beatles - The White Album (1968)
Pink Floyd - The Wall (1979)
These are the two studio double albums of both bands. I prefer the White Album, though The Wall may be more popular.
The Beatles - Let It Be (1970)
Pink Floyd - The Final Cut (1983)
Beatles win out here.
The Beatles - Abbey Road (1969) - really their last recorded work
Pink Floyd - All the albums they've recorded since 1983 combined.....
The Beatles win that one
Anyway this was just a fun exercise, it's not exact. But don't mind me.