Let's use the Martin dreadnought as an example. 

First image is a 1933 D-18. 19 frets, 12 clear of the body. Please note the elegant 4-piece top!

The second image is what they did to get 14 frets clear: they shortened the body...

And then in image #3, you see they made the fingerboard one fret longer, moving the soundhole and pickguard closer to the bridge. That's about it.

OK, now here's what else they might have done to get 14 frets clear of the body.

Again, image #1 is our old friend, the '33 D-18. (All these employ the same scale length.)

In image #2, we see an imaginary D-18 (thanks, Photoshop!) where the fingerboard, bridge and soundhole are all moved north far enough to reveal 14 frets. It looks rather odd, eh? Kinda like a Gibson J-50?

Image #3 shows one more fret, with the soundhole and pickguard moved south. This is what Gibson did to make their original Jumbo guitars like the J-45 and the SJ. Ironically, Martin recently offered a 14-fret slope-D, copying Gibson's remake of their own guitar from 70 years earlier! 

Consider the tonal effect of the placement of the bridge closer to the waist of the guitar, regardless of brace position underneath, which as another discussion. 

These same principles also applied to the 12-fret 000 as it evolved first to the OM (14 fret with the original 000 scale of 25.4") and then to the eventual 14-fret 000 which had a 24.9" scale.

Here's one of Gibson's earlier true flattops, a 1929 L-1. 19 frets, 12 clear, 24.9" scale. Check the bridge placement, check the soundhole placement. The first Nick Lucas Specials were based on this model, ironically known now as the Robert Johnson guitar.
 

These guitars might have sounded good if they had been braced differently. As it was, they were generally unremarkable. They had two longitudinal tone bars, much like the bass bars in violins. It was a sound, but not a great sound. 
 

Remember Gibson started with archtops, and only gradually moved into the flattop realm, hence the elevated pickguard.
 
 
 
 

Here's a predecessor to the L-1, a 1928 Nick Lucas with a shortened 19-fret board, and f-holes. Note the even lower bridge placement, below the wide spot at the center of the lower bout, which indicates a longer scale (not sure what it is though).
 
 
 
 
 
 
 
 
 
 

Remember that the only real difference between a Nick Lucas and the other production Gibsons of the day (aside from decoration) was the body depth:

The simplest way to quantify the effect of the deeper box is that it enhances the lower frequencies. There a numerous examples of this on the market besides the historical Gibson efforts. Martin makes two guitars with both shallow and deep boxes, the most notable being their 0000 (occasionally known as style M), and its deeper version , the style J. They have made thousands of each in every imaginable material combination, and just that model offers a good direct understanding of the effect of a deep box. 

Another Martin model is their 00 "girl guitar," the 00-16DB (as in: Deep Body), introduced at NAMM in 1997 and sporadically offered in a variety of woods with their "custom classical wooden mosaic rosette," which, alas, is visually rather overpowering. This guitar was originally released with a spruce top. It is effectively their version of the Nick Lucas. Have a look at it here if you like.

A curious other Martin model is their 000NB, Norman Blake's remake of the 14-fret 000 as a 12-fret guitar. Reverse evolution of a curious sort. Employing the same rationale I used for the H-13 SCGC, it kind of looks like this:

Notice the bridge and soundhole position. Notice also that it seems to be a lefty model! Huh?

I think I prefer the original 12-fret 000 for both sound and aesthetics.

The first one, from 1931, has 12 frets, and represents (to me) the epitome of this model: bridge and soundhole are absolutely correct. This is an odd photo, somewhat foreshortened.

The tailpiece model to the right has 13 frets, so the bridge is moved up - but the soundhole location remains the same. Check the distance between the end of the board and the soundhole. (I own a 13-fret Nick Lucas that evidently once had a tailpiece on it, but never a pickguard, and the pin bridge is factory original. It dates to 1929, and like this one is rosewood.)

The point here is that Gibson gained more frets clear of the body by moving the bridge and the fingerboard north.

Here's another example, the end of the line for the Kalamazoo Nick Lucas guitars: 14 frets, same old 24.9" scale. See how the bridge is even closer to the waist now, and the soundhole is pushed up. 

The Montana Nick Lucases have been different: some have a 25.4" scale and 14 frets. 

Does this have an effect on the sound? I think it does.

The SCGC Model H is my attempt to combine the optimal bridge and soundhole location of the 12-fret with a 25.4" scale, which I think sounds better and is easier to tune. 

The result is a 13-fret neck guitar. 

Read more about that here.