The active EMGs have fewer turns of wire in the coil, their original designs actually including a preamp in the shell. These fewer turns result in a low enough output to require this powered (from the 9- or 18-volt battery assembly) setup to present a strong enough signal to the preamp section of your amp. These can then be run thru EMG's BTS/BTC networks or any of their accessory tone modifiers built into the bass.
The HZ EMG's can be wired up with regular pots if need be and run exactly like 'regular' Fender or Gibson pickups. They can also be run into 9- or 18-volt tone networks as well, and this is where you see the 'passive pickup/active electronics' setup you're talking about.
The real difference in the real world (tone preferences aside) is that the HZ pickups obviously have enough turns of wire to make enough output on their own, but they can potentially be noisier because of that, and that noise will be amplified by the add-on active tone network. In my experience, the true active EMGs are deathly quiet. And they are internally grounded: This eliminates that ground wire back to the bridge you'll need with HZ pickups, largely increasing the chance of getting bit by the mic if your grounds are all over the place in a crummy electrical environment ! Also, since the preamp is shielded in the shell, I've owned very quiet EMG basses that had no shielding in the control cavity at all, a truly strange sight. You could never do that with passive pickups.
If you're familiar with mics, think of it this way: High impedance picups are like so-called 'dynamic' mics; low impedance pickups are phantom-powered, just like that kind of mic, whether it's the 1 or 2 9v batteries, or the rack-mount power supply of the Alembic Series axes.
Or think of it this way: You COULD run EMG low impedance pickups and the high impedance ones with a preamp in the shell. You could NOT do the same thing without preamps.
And bear in mind, the use of the terms 'low' or 'high' impedance, or 'active' or 'passive' is very loose. I only used EMG as an example as I've a lot of experience with them. Other brands would require some homework for me to give you a proper answer.
J o e y
