What makes speaker's sound big?

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.

High Fidelity Cables NPS-1260 3D Enhancer >>>Game-Changer 
 
https://www.youtube.com/watch?v=wliupB_i5JY

This thread keeps going...So here's another thought, not specific to the speakers the OP mentions. 

(Again, the real answer is undistorted, real full range loudspeakers/subs. Size does not matter, but actually achieving the above sentence IS certainly easier with physically larger speakers. At least at lower cost.)

However, nobody SHOULD want big sounding speakers. I'll even go further. No one should want speakers to CREATE scale and sound big. A speaker reproducing stereo (almost by definition) should simply disappear!

Yes, room reflections, speaker style, on and on are important, but none exclusively provide or control auditory image-size and scale. 

Let's back up. What is the recording? A piccolo solo? A floor to ceiling piccolo would be undesirable, even comical. A bumble bee buzzing around? Small, precise image flying around.

Two of the DIRECT causes of image-size and scale are 1) Volume and 2) the Recording itself. 

If your speakers are making, "small things" big, you have a problem. Wiring a driver out-of phase and increasing the level (to that driver) could create an artificially huge image. Phil Specter's Wall of sound and many, many recording use the concept to successfully creat big, enveloping sound. Echo, reverb, phase are the tools engineers use daily to give your music scale! So the bottom line is: image size should be proportional to the recording. Your volume knob is your one real control--the louder, the larger things should sound. Magical recordings do it all: huge performance space, big scale, precise imaging, dynamic--the engineer gives you the majestic illusion of large sound. Thank him or her. Now go play with your knob.