Good question. Staggering crossovers can have very good effects, especially when a 1st or 2nd order slope is used. Crossovers are not brick wall filters. They roll off frequency response as follows: 6db/octave (1st order), 12db/octave (2nd order), 18db/oct. (3rd order), 24db/oct. (4th order), 36db/oct. (5th order), 48db/oct. (7th order)
80hz-160hz is once octave, just as 1000hz-2000hz is one octave.
What those things mean is this:
Say you have a full range pink noise signal at 100db. If our crossover point is 80hz with a 3rd order 18db/oct. low pass filter, the signal will be down to 82db at 160hz. Although this signal is rolled off signicicantly it is still audible if no other full range signals are present. One can test this by having all the speakers except for the sub woofer turned off and run a frequency sweep through the system.
Staggering crossovers will allow you to reduce the level of the signal after the crossover point, effectively steepening the crossover slope.
Say one has a receiver and it only utilizes a 12db/oct. low pass crossover. With an 80hz crossover point the signal is still at 88db at 160hz. At the -6db point of 120hz the signal is still at 94db. Let's say the subwoofer has a 12db/oct. as well. Staggering the sub's crossover at 100hz would allow the sub's response to now be down -19.2db at the 160hz point rather than -12db and down -8.4db or 91.6db at 120hz. Essentially it allows a 12db/oct. roll off from 80hz-100hz and then a 24db oct. roll off from 100 hz on up. It may allow for the system to blend together in a better manner.
Most receivers nowdays utilize a 18db/oct. slope and sometimes a 24db/oct. slope for the sub crossover. In this case, it may not be necessary to stagger crossovers. Depending upon the system and how it integrates with the room, a staggered slope can be advantageous.
