I've never heard a sound difference between types of wood in non-walled enclosures. Usually it's a weight thing. It's usually a birch vs MDF comparison. Birch is just better quality, lighter, stronger. MDF will almost always work, but MDF can have symptoms that other wood types don't have.
Bracing is usually stronger than more layers of wood. Resonance is the killer. Resonance is why you need bracing on certain pieces in certain locations. Resonance can store energy and build up over time, and that constant vibration is what can break a box apart over time. Like I design my boxes to last, be durable. A lot of my designs could function without some of the bracing, but walls would flex and put a lot of fatigue on the glued joints and surrounding areas. Sometimes it doesn't matter quite how thick a wall is, if it's too long, it has to be braced. Like a side wall that's 40" long and fairly tall needs to be braced because that long distance is a lot of leverage and that piece will flex a lot. The fact that sounds waves are a mechanical (kinetic) AC wave means that the cycling can store energy into material it's being transferred too, as long as the wave is still currently active. Sometimes that energy can build up to a breaking point and cause a box material failure, same thing with the metal on your car. AC pressure is way different than you standing on the box and gravity causing your weight on the box. But that's why wood is used a lot for audio enclosures, it doesn't resonate very well, as a material. You're not making a tuning fork out of wood. Has to do with molecular composition and geometry
Sounds is a wave, and waves have certain lengths. Physical material also has certain lengths. When the sound wave's and material's characteristics match up, that's how you get resonance. The lower the frequency, the bigger the object you resonate with. The higher the frequency, the smaller of the object you resonate with. I'm saying all of this to try to explain why box bracing is important when it comes to wood thickness. If you study large bridge engineering, old bridges used to get knocked down because the wind would cause the bridge to vibrate at the resonance frequency of the bridge (long bridge, low resonance). The resonant energy would build up to a point that the bridge would literally start looking like a sine wave, and then it would completely fall apart. Just a little bit of wind could do that, and it's because of how resonant energy can become stored in physical material. And that's why bridges are braced like they are today, is because of resonance. You know, now imagine the wind from a 150db+ sound system. All that flexing to the box and to the vehicle causes fatigue and generally a loss of sound pressure.