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Actually, what Rick said is one of the keys:
"Brace shaping and carving affects how the top breaks up into vibrational modal patterns. "
In terms of the tone, the guitar _is_ those modal patterns, and the shapes, frequencies, and damping of those modes are what you control to 'shape' the sound. There are real limits to our understanding of this: much of the variation between guitars seems to be in those modes that happen at high frequencies, and are hard to 'see'without lasers and optical methods. Still, even the lower modes that we can see easily have effects.
Most of the actual power produced is the result of the top moving in and out like a loudspeaker cone. The resonant pattern of this shape is the 'main top' mode, and usually occurs around 200 Hz; say the pitch of the open G string. That just means that it's easier to drive the top this way at that pitch than any other, not that it only happens there. This mode has a long 'tail' into the upper frequency regions: it's still producing more sound at 1000 Hz than any of the resonant patterns near that frequency.
There are two reasons for this: those higher-order modes tend to involve small areas (think, 'transistor radio' against '15" woofer'), but, more importantly, they each involve a _lot_ of small areas. There's a lot of 'phase cancellation' going on in those higher modes, with the air 'sloshing' back and forth and not really making any noise for you. This is worse, for a variety of reasons, in the lower 'multipole modes', such as the 'cross dipole' and 'long dipole' modes that are just a bit higher in pitch than the 'main top' mode that's doing most of the work.
If you look at the patterns of these modes, and think about where the stiffness of the bracing is, you can see what effects different styles of brace shaping will have. To look at just two: the 'main top' mode is moving and bending a lot in the middle, with much less bending as you get closer to the edges. The 'cross dipole' mode, in which the two ends of the bridge move up and down out of phase, rocking across the center line of the top, shows a lot of bending near the bridge ends, and none at all in the center of the top.
So, let's start with 'straight' bracing: uniform height all the way along until you taper it down near the ends, as our 'norm'. If you scallop that bracing you're reducing stiffness in the center, which will drop the pitch of the 'main top' mode, but you don't take much wood off where the 'cross dipole' bending is going on. Tapered bracing works the other way; dropping the 'cross dipole' for little, if any, change in the 'main top' pitch and activity.
What does this mean in terms of tone? Well, remember, the 'cross dipole' is much less effective at producing sound than the 'main top' mode. If the dipole comes in close to the main mode in frequency it will tend to 'steal' energy from the 'main top' vibration, with the result that the spectrum of the guitar will 'fall off' quickly above the tall 'main top' peak. This tends to give a 'sharp', 'bright' or 'cutting' sound, so tapering the braces tends to go in that direction. Scalloping them increases the pitch seperation between the 'main top' and 'cross dipole' mode frequencies, and thus increases both the height and width of the 'main top' peak in the output. The tone tends to be 'warm', 'full' or 'bassy', but perhaps lacking in 'clarity'. The extra amplitude gives you a lot of 'punch'.
This is just one exapmle, and only the beginnings of it: you need to think about all of the things that the guitar is doing to get a real picture of what the tonal effects of any particular brace profile will be. And, of course, it's all relative: scalloped braces on a Parlor sound a lot different from the same profile on a Dread, because the 'balance' of the design is different: 'bass' has a different meaning.
Ultimately, as I said, you have to look at brace profile as one of a number of variables that you juggle to get the sound you want. There are no absolutely 'correct' answers, only relatively 'better' or 'worse' ones depending on what you're trying to do.
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