While I was composing this reply I realized I'd already said most of what I know earlier in the thread.
I believe most "active" instruments only have one or two opamp chips in them which is enough to boost the pickup's output slightly and change the instruments output impedance making it easier to get a bigger sound down the guitar cable. (I'm mostly making this up so bear with me). A setup like that is probably happy with the power supplied by a single 9V battery, and with pretty good battery life. Think of it like a "buffer" pedal for a pedalboard.
But the preamp board on our Series instruments has 5 opamp chips and 3 FETs which all need power. As I said earlier, the 5534s can operate in wide range of power supply voltage anything from +/-2V to +/-22V. Our double-9V batteries provide +/-9 and the DS-5 is closer to +/-18.
Now consider playing through a small 40W amplifier. It would sound great up to a certain level of volume and then it would start to suffer, likely "clipping" off the transients or biggest peaks of the audio waveforms. But achieving the same
volume using a 100W amp would likely reproduce a clean sound. Playing through a poweramp rated at 400W which is just cruising along would yield better results than playing through a 100W amp that is maxed out and nearing it's limits. If we scale down that idea, I believe our Series boards can provide their cleanest and most powerful output when powered with the higher supply voltage.
I'm sure I'm oversimplifying it but if anybody asks you that question again, the simple answer is "
Headroom".
Jimmy J