As has been mentioned, your Alembic has output level trim pots so the active output level can be set to whatever level you like. It's probably set low now, or your battery is weak if the output level is low relative to a passive bass.
If you set the output level too high, you may overdrive your preamp and get a distorted tone at all volume levels. This was why Hartke added the active input - it has less gain, so the hotter signal won't overdrive the preamp. If you plugged your passive bass in there, it might not be able to generate enough input to drive the power amp to full power.
The pad circuit on most instrument amps is very simple - just pair of resistors. The input impedance (you can think of impedance as AC resistance although it's actually more complex than a variant of DC resistance) may be slightly different at the two inputs, but won't be significantly different.
Your brain perceives things in interesting ways. By nature, if two things are close to each other in volume, you will almost always prefer the louder one, even if the sound quality of the softer one is better.
Modern amps have a lot of dynamic range at the inputs, so you can use the passive input unless it sounds distorted when you are playing harder at the bass. If you were playing a 1960's Ampeg B-15, you might find it hard to get a clean signal with a modern active bass - the output level is just too high. The good part about active instruments is that you can turn the volume down at the bass with no change in tone.
If you used level-sensitive effects (like an envelope follower or compressor) in your signal chain, then it's great to have the output level trimpots, so you can set your Alembic up to match the output of your passive bass. If you didn't, then you'd have to reset all your effects when you switched basses.
Impedance matching can affect the tone of your instrument, but is not a factor for the passive/active inputs or your instruments. High frequency signals (like your cable TV feed) have very specific requirements for each part of the system to insure minimal signal loss, including very specific input impedances. Audio-type systems work on a different principle, where you want to have the input impedance of the preamp significantly higher than the output impedance of the pickup or microphone. The output impedance of a passive pickup would be on the order of a couple thousand ohms; from your active circuit, tens to hundreds of ohms. The input impedance of a normal amp will be 50-100K ohms, so there shouldn't be an issue in either case. Impedances will come into play when you have a very, very high impedance pickup like a piezo. They will often have output impedances in the millions of ohms, which is higher than a regular guitar amp input impedance. In this case, the effect will be to filter out the bass, which is why some acoustic guitars sound scratchy and thin when they're plugged into an instrument amp. You don't see this much anymore because they put a suitable preamp in the guitar now which solves the impedance mismatch.
David Fung
