You have a number of factors, and I'm not even sure I even know them all.
For explosives like fireworks, one issue is pressure -- larger fireworks tend to have thicker shells, and be wound more times. (in the manufacture of larger fireworks, they wrap them tightly with string to compress them and make them burst further). So, when the firework finally bursts, the internal pressure is higher, and so you'd end up disturbing a larger volume of air in the same amount of time. I have no idea how much this is a factor ... I assume you've have to take an identical amount of explosive, in identical volume containers of different strengths.
Obviously, using more explosives would also result in disturbing more air, but I don't know how much of a contributing factor volume is vs. pressure.
One other factor is the chemical used in the explosion -- obviously, different ones burn differently, but even in the case of balloons bursting, and we're dealing with similar pressures of similar sizes, helium and hydrogen don't make the same sounds as something filled with compressed "air" ... but I don't know if it's an issue with the molecules being smaller, and so less likely to vibrate other things they pass by (just by odds of there being a collision), or if it's simply an issue of different total mass, and so there's less stored energy at the time of release.
I'm guessing shape is also a factor, but that's going to be even harder to quantify, as with a shaped charge you're going to have gas moving at different speeds in different directions, which may make the pitch vary with the location of the observer.