Bigger drivers = bigger soundstage


Ideally, I don’t like to be aware of a speakers location in a room and like having sound being well centered for tv/movie listening.  I have two listening rooms and the one with larger drivers (older) fills room so much better vs better speakers (newer) with smaller drivers.  Room acoustics favor larger driver speakers.  
Seems dispersion is better.  The larger driver speakers do not image as well but very enjoyable to listen too. 
So now I am upgrading the smaller driver speakers to better and larger driver speakers and it follows a larger speaker cabinet also occurs.

all speakers herein are from same manuf. 
emergingsoul
So many rabbit holes herein. All worthy of explanation.  So much so hard to follow.

speaker designers will tell you it’s hit or miss when putting it all together.  
A rigid heavy speaker with ample cabinet room behind a driver with a mounting structure that don’t resonate, is key to transmitting sound.  Larger bass drivers help if they don’t distort, too small ain’t good.  A shoebox size speaker is clearly too small. 
The OP headline doesn’t gel all that well with the described findings, it seems. Too many factors are at play determining "bigger soundstage" than mere driver size alone, though better "room fill" is more in line with the use of larger drivers/overall, summed radiation area. Larger radiation area to me generally is about better scaling (which, admittedly, is an aspect of soundstage presentation) and an added sensation of density, impact and ease.

As pointed out by Duke larger drivers have a narrower dispersion pattern, and especially when coupled to horns the sonic marker of this is intensified. As to multiple smaller drivers vs. a single larger one (per channel) a line array of smaller woofers/mids would act as such and limit vertical dispersion, whereas a single, larger driver acts as a point source with narrow dispersion overall. I’ve never much cared for the sound of the multiple smaller driver configuration vs. a single larger one, but whether that comes down to the dispersive nature mostly or other I couldn’t say (I do prefer what emulates a point source presentation over a line source ditto).

Typically the use of smaller drivers involve low sensitivity designs, where the larger driver designs I'm thinking of use high sensitivity units - this is not insignificant either; used within their upper band confines, not least when high-passed down low (which may be a given in the first place as such drivers are usually LF-limited, and thus in the need of subs augmentation), a high eff. large driver sports very low distortion and ample headroom with limited cone movement and inertia build-up. Smaller, low eff. drivers, even in multiples, simply can’t replicate these traits, though they’ll extend higher. Personally though I’d go for a lower cross-over in the ~800-1.2kHz region (with 12-15" units) and have one large driver (or the same in duals) cover the "power region" down ~100Hz, give or take, and avoid a x-over in the upper midrange typically found with smaller drivers. One could also use smaller drivers (8-10") in the same frequency span - say, in a D’Appolito config. - and have very respectable results as well, such as found with the (sadly now defunct) S.P. Technology speakers (by Bob Smith) in conjunction with a waveguide.
There is so much more to that than just the driver size...
Longer time ago I had a smaller room, smth like 8’4 by 14’, 10’4 ceiling, old apartment building. It could be filled by bookshelves with 6” drivers. Floorstanders with 10” were just too much. I sold the floorstanders to a friend, in his approx 16’ by 17’ by 9’6 from they are much better (even when poorly placed).
my current room is 21’ by 23’, 8’4 ceiling with 7’ by 10’ opening to above + two other openings effectively increasing the volume by some 50%. Used Lowther Fidelios for a time, poor bass with solid state, adequate with 300B SET. That’s 8” + folded rear horn.
Acquired ancient yet immaculate MBL 101c. Base drivers is approx. 9” diameter, probably 13” tall, radially pulsating elongated aluminium ellipsoid. Deepest bass was lacking, but the room was filled so much better than with Lowthers. MBLs need ML 23 to come alive, less power and control is not for them. Wanted cleaner bass, got Gradient 1.5 Helsinki. Got the clean bass (not very much of it though). Overall, almost ‘near field’ listening - truly amazing in the sweet spot, adequate background music in the whole room, yet no freedom of movement like with the MBLs.
Decided to build dipole subs “a la Celestion 6000”, got some BMS 18N862 drivers. Connected them straight to power amp (naked drivers on the floor). 18” drivers, so no heights, on the floor, so terrible early reflections - yet smth. very immediate, coherent, and “right”. Added BSS 966, lifted lows (dipole correction) and heights. Not perfect, but good enough to make me wonder why people insist on boxes, and am I really in a hurry to complete the project as intended. And I have only connected one pair of those BMS, with two per side there will be no shortage of sufficiently deep, yet clean and dry bass. But BMSs do not fill the room. I absolutely need to add omnidirectional speakers from 200 Hz (I.e., above room modes).
I will have two options for omnidirectional, MBLs and German Physiks DDD drivers. When I make ‘enclosures’ for DDDs, I will see if size matters (MBLs have much larger total radiating surface).