..... Originally the 870 12, 16, and 20 gauges were built on the same frame size. Somewhere (I think around the time the Express version was introduced) they came out with the LW versions and the 20 gauge was (and still is) built on a smaller frame. The 16 is still built on the 12 gauge frame. I'm not positive on the 28 gauge and .410 bore versions so will not comment on them .....
I can't comment on the Mossbergs as "I don't know about them!" But Remington M870's .....
Until 1972/1973/1974 or thereabouts, Remington made 12, 16 and 20 gauge pumpers on the same size of receivers (outside dimensions; length, width, height). But then Green came out with their lightweight M1100 and lightweight M870. I didn't follow or keep up with the M1100's until later, but .....
Remington did and still does build their LtWt 20 gauges (Express and Wingmaster) on a narrower piece of billet steel than the 12 gauge and 16 gauge.
*** That narrower piece of 'billet' is also the same size they make their "small gauge" .410 and 28 gauges on, and even the Model Six/7600 rifles! I know this to be correct because I've swapped [synthetic] stocks (and folders) between a M7600 and ltwt 20ga M870.
*** Once upon a time (to digress) I wanted (lusted?) after a 16ga Browning Citori @1996 or so. They built their limited rum of 16ga O/U's on a 20ga size frame, but I never followed up and bought one of those Browning 16's.
Those thoughts though, helped influence my disappointment when Remington built their M870 16ga on a twelve gauge frame! Which I thought was pretty dumb and helped insure interest in 16-870's would be
short-lived! Which prooved to be the case! Those
Browning 16 Lightning Citori's though, are prized and bring a good price.
Like the .41 Magnum and .358Winnie, the 16gagger is one of those purfekt cat-tri-juz the publik somehow missed.
But back to LightWeight 20gagg M870's,
I love mine.

And while .410 and 28gaggers aren't often sought on any of the Remington LtWt's, Owners of those smaller
M870's and M110's speak well of their's!