What makes speaker's sound big?

One factor no one has mentioned is the quality of the music coming from your source. Better quality source components can make the same music (whether from vinyl or digital) sound fuller and with more presence.

Amplifiers can also make the same speaker sound fuller in sound.

I had my custom moderate size listening room designed to accommodate 6-12" woofers at high efficiency, 98db.  Now I get 25 Hz down just a few db.  Bass is not an issue.  This is very superior to my prior room which was 25' X 20' X 11.5' where I only got 35 Hz and bass response sounded heavy and uneven.   The quality of the sound is 100% more satisfying/dense/rich with the same equipment.  I also use acoustic tweaks including a double pair of Hallographs and a slew of SR HFTs, some ECTs and GCTs.  I don't claim to get the best sound I ever heard but sound that one has difficulty leaving the room or running to the room to get to the music.   I've heard 100s of systems over the years.   The $1 million VAC/Von Schweikert system sounded the most life like.   That system was large in a very large room but provided whatever the character of the recording, close or distant with all the ambiance that was recorded (or reverbed).   It also provides a bubble of sound that emanates so that it spreads throughout the room, unlike most box speakers and many stats I've had.   Advanced box speaker technology can rival any other tech design.   It can be costly.   I can make do for now with a great room and very good speakers that bring me to the music as it was recorded, near, far, in-between.   Music can literally pop out at me, at all frequencies, just like live music at all levels of dynamics.   Only orchestral music sounds compressed to some extent, often the recordings' fault as well.

Big sound?
It won’t be easy to find but Apogee Diva will do. Not just big, but amazingly realistic sound.

audio2design
You are exactly correct. All of these issues and many more make the difference. 

I also have a single driver LII Audio Fast 8

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I have this  fast8 arriving in 2 weeks, I just surveyed several LII 10's and 8's on YT vids, ,,seems a  tad warm in the critical mids,,But we'll see after i build the cabinets, Will uploada  YT vid,
Now to answer the OP, 
The answer he is looking for is
~~Sensitivity~~~
The Thors with 87db sound like a wet blanket
's been thrown over the speaker, LITERALLY!!!!
Vs a  relatively high sens at 91db FR Diatone 6.5 wide band. 
The Diatone 91db sounds bigger vs the MTM Thors, 
Go figure, db sens is everything in a  speaker, 
Lower the db more ouny sounding speaker, higher the db la mas grande the image. 
Its that simple.