The majority of basses that I've had where active. But I don't choose a bass because it's active or passive. I choose it because I wanted it. And it happened to be active. But I find that the basses I prefer aren't offered in a passive version. An advantage of active is that they have a midrange EQ. Whereas passive doesn't.
This is because there was a time in the '80s and '90s when people generally thought an active bass always had higher output levels than a passive bass. It's not always true though! There are some very high output passive instruments, and some surprisingly low-output active ones, and everything in between.
My Precision one such machine. It has a regular precision pickup, a regular volume control and a regular passive tone control - it behaves and sounds like a regular P Bass. But with the flip of a switch I can engage the active section with added bass and treble boost/cut. Why would anyone have to choose an active vs a passive bass?

Active DI's present a different load to the pickups/electronics of the bass that CAN effect the tone. Some electronics handle the loads better than others. If your bass sounds "thin and weak" with a passive you can try a better passive DI. As GeriO pointed out, they are not all equal.

I played active basses pretty much exclusively for the past 10 years or so, but in the last 6 months I've realised that passive basses with traditional Alnico pickups have a certain organic purity, response and depth of tone that I was not getting from active basses. I think an onboard preamp naturally adds a certain compression to the sound also.

CONTROLS: Volume, pickup blend, three-band active EQ (1x mids boost/cut pot, 1x stacked treble/bass boost/cut pot), active/passive toggle switch HARDWARE: Fender tuners, HiMass bridge FINISH: Olympic Pearl, 3-Color Sunburst, Belair Blue, Aged Candy Apple Red (reviewed)

premierguitar. Squier Contemporary Active Jazz Bass HH Review. Recorded direct into Focusrite Saffire 6 interface into MacBook Pro using GarageBand. Clip 1: Riff with both pickups engaged, followed by neck pickup only, then bridge pickup only. Tone at 70 percent, slight bass boost. Clip 2: Slap riff with both pickups engaged. Am experimenting some, and slowly accumulating several to go on a future pedal board. I just got a new Mooer Envelope Filter auto wah. It is billed as being both for guitar and bass. It got very high ratings, but most of those were from guitar players. I have tried it on three different active basses, and can hardly get any wah out of it.
SWR partnered with Marcus Miller - arguably the most influential bassist of his generation -- to create the ultimate tool for bassists. Or as Marcus calls it
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