It all depends on the design of the entire circuit and the intent of the player using the bass and all related elements of the signal chain. Active basses can sound 'warm, round, and vintage' too depending on how the tone controls are utilized, but it depends on the aim of the preamp (and pickup) design and how it all interacts. There are no 'absolutes' one way or another. What I can say for sure is that whether it's an onboard preamp in an active bass, or an outboard unit that you plug a passive bass into (like a Sadowsky outboard pre or even an Aguilar Tone Hammer), the whole idea is for the preamp circuit to affect the sound of the bass in some way.... otherwise, why are you using it?
For starters, one could use or intend to use a preamp (onboard the bass or not) to simply boost signal with no other intention- if the preamp can do that, but also being aware that adding to or changing a circuit, internal to the bass or externally may do more than (simply) boosting a signal and may also unavoidably change the sound maybe in the ways intended and ways tolerable... or way unintended and not tolerable.
If I want to play warmly, roundly and with vintage tone, I'm going to find a way to make that sound come out of the speakers of the amplifier. If I want bright, zingy, and with piano-like brilliance, there are other requirements that are beyond my ability to twist knobs or change my technique/approach. Number one among them is clean/new roundwounds. Another thing is a cabinet with a tweeter, and ideally main speaker setup that has more 10 or 12 inch speakers and less 15 inch speakers. So I have to start from the position of bright, clean and with piano-like sparkly brilliance, and then find the warm tones from there. I have never found it possible to go the other direction- bass with dirty, dead strings and wooly-sounding amp with one or two 15 inch speakers and no tweeter and yet still finding those Marcus Miller/Level 42 slap tones.
So, in my opinion and my experience, it comes back to your first sentence.