As @John_E said, it depends. I feel as if active circuits give a “thicker” tone, as if the frequencies aren’t that scraggly. Maybe you know what I mean.
Other than that, I’m happy to play passive and I find it hilarious that the batteries drain when you leave actives plugged in. Is that the case when you have an active/passive switch and set it to passive, too?
Cheers Antonio
That’s so funny, I don’t like exposed pole pieces - just a hazard for when you slap too hard. 
Passive. I guess that’s my only preference. This is because I can’t imagine putting a battery in a guitar as if it were a remote control. Sorry, no 
(And knowing myself, I’d have to think ahead and buy a whole supply of these batteries as it is something I always miss and always forget to have spares…)
Believe it or not, some basses actually require TWO batteries 
Always a sensible thing to do!
I have one passive bass and six active basses (one of which is active ONLY!).
Why active? I think @howard once said (and I am at minimum paraphrasing here, and potentially mis-quoting): EQ on the amp is for adjusting to the venue, EQ on a pre-amp pedal is for adjusting to (general) personal preference, and EQ on the bass (i.e., using the active part) is for on-the-fly adjustments within a song or between songs.
In a live setting, I wouldn’t want to fiddle with my amp six feet away or the knobs on a pedal on the floor. Also, in certain cases, there isn’t even an amp - just a PA.
“Active or passive?”
Yes, please.
To be fair a tone knob or volume control (in case of a jazz bass) does work too. An active with EQ is more versatile ofc.
Usually an active bass is more expensive.
You are right, of course! I wasn’t entirely fair in my statement. But, active EQs are clearly offering a wider range of options 
And often, to me, significantly betterer.
Potentially un-possible to gauge though
Not by meeee. 
If I hear it and I like it, it’s a keeper.
We can’t tuna fish or hear with others’ ears.
But we can enjoy a sandwich while we listen to something that sounds personally pleasant. 
Like a creek, fireplace or rain. 
I’ve seen fire and I’ve seen rain. 
Me too and is the reason why the answer to the original poster’s question is the ever so often, it depends.
My latest addition to my collection is a Yamaha TRBX504 with both passive and active circuits, my first bass with both. To my (half deaf, tinnitus-suffering) ears, there is definitely a difference, and it depends on what I’m playing as to which I’ll use. The active circuit has more punch and upper end, where the passive, more mellow and deeper. Not a huge amount, but enough that you can hear the difference.
I can tell the difference on a Cort B4 artisan element, much like in the same way @OldBlue stated previously, apart from the deeper tone in passive. I’ve found this useful for certain songs to change my tone a bit without having to adjust anything else, but not that much. Overall, I tend to let the switch off and stay in passive most of the time.
I wanna know have you ever seen the rain?
See above. 
Not lately, though. 
Upon us all, a little rain must fall
Yes indeed there is a difference in passive and active on the same bass - the biggest of which is gain (volume) which can trick our ears into “better”.
Any other difference is the preamp’s tone coloration.
The Glockenklang preamp (best name ever) is super clean and with the eq at center, offers nothing - but gain. Which can again sound like it’s bringing things out but really just making things louder, which makes the bass feel like more punch or responsiveness etc.
I’ll go back to Fine Corinthian Leather once again - it’s only important if it’s important to you.
