My main bass is as Warmoth Deluxe 5 with a Seymour Duncan MM Alnico pickup and an active / passive switch and I've recently put together for a friend a passive Dinky-P with the same pickup (4-string version). These pickups are definitely passive and in fact fairly hot, maybe like a vintage P-bass or so, and they are supposed to be a direct replacement for the originals, so I'm sure those must work ok as passive too.
As for the sound, the difference between active with the eq flat and passive is very subtle, just a touch less treble, so I'm not sure the reason your new P is so much better than your actives is that it's passive, it's more likely a matter of woods and pickups. In any case the mod is cheap and easy, so it's probably worth giving it a try.