This gets very complicated. The only way to approach it is to think about what happpens when you change _one_ thing, and leave everything else alone. So..
30+ years ago, Fred Dickens made a classical guitar that was, iirc, about 6" deep. After he'd played it for a bit, and made some measurements, he cut the sides down by about an inch, and put the back on it again. He kept doing that until he'd gotten it down to less than 3" deep. The result was that the 'main air' resonant pitch rose by (drum roll) 7%; a little more than a semitone.
Yes, it's true that the _Helmholtz_ resonant pitch of a deeper box will be lower. However, the 'main air' pitch on a guitar, that corresponds with that, is actuallly the lower part of a 'bass reflex couple' which involves the top and back as well as the air. The 'main air' pitch is actually a good bit lower than the 'Helmholtz' resonance of the same box with rigid walls, as Rossing showed by burying guitars in sand while leaving the soundholes free. The difference between the 'Helmholz' and 'main air' pitches is governed by how strongly the top motion and the air pressure change in the box are coupled. With a deeper box you get less air pressure change for a given amount of top motion, so the coupling is less, and the frequency difference is not as great.
In Fred's experiment, then, as he cut down the sides the coupling between the top and the inside air pressure increased. This shifted the 'main air' pitch downward more as the body got shallower. At the same time, of course, the shallower body had a higher 'Helmholtz' pitch. In the end, the stronger coupling almost made up for the rise in Helmholtz pitch, and the 'main air' resonance hardly changed.
Note that the coupling that shifts the air pitch downward also shifts the top pitch up. Making the body shallower could conceivably cause the 'main top' resonance, the other half of the 'bass reflex couple', to _rise_ in pitch, even though you haven't done a thing to the top. If Fred measured that, I haven't seen the data: I'm pretty sure he published it before I joined the Catgut Society, and he never mentioned it in any conversation we had.
Making the body deeper decreases the height of the 'main air' peak in the output spectrum, all else equal. In effect it seems to 'spread out' the bass response: you're less likely to get a really strong note at that 'main air' pitch (which is often the 'wolf' down around G on the low E), but overall the bass range is smoother.
It's likely that the 'main top' resonant peak is also a bit more sharply defined in the shallower boxes. It's been found in studies of classical guitars that a tall, sharp 'main top' peak in the output tends to sound 'cutting' or even 'harsh', depending. I'll note that Flamenco makers do a number of things that tend to make that 'main top' peak tall, and they need the added 'cut'. Some of the guitars that the delta blues players liked were also shallow and small; useful in a noisy party environment.
Making the top bigger while keeping the same body depth has somewhat the same effect as making the box shallower. However, a big top does work a bit differently from a small one. In particular, because you have to beef up the structure a bit on the wider span the area of the top increases more slowly than the weight: the ratio of area to mass is lower for a larger top in general. This tends to give less output. The larger box is also going to be more 'bass balanced': not that a big guitar can't have good trebles, but the balance between treble and bass overall tends to be effected. Since our ears are less sensitive to lower pitched sounds any added power in the bass for the bigger top tends to be less noticable than it would have been. Overall, then, it's easier to make a loud small guitar than a loud big one.
There are lots of other variables in here; soundhole size and location, for example. If you look closely you'll see that many of the possible options have been tried already, and some of them work well in specific applications. Consider _why_ that might be, and make your design changes accordingly.
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