Do you want to get the "sound" that your upright bass hero does? It's easy! Just play like Ray Brown.
Now, that's a snarky way of saying that the source of the sound is almost always the player. To get Ray's sound, the most valuable things that you could add in order to get that sound would be Ray's bass and Ray's hands. Sure, equipment matters, but it doesn't "create" the sound the same way that electric bass guitars and rigs often do. And even on electric, the player is still the "magic ingredient." For instance, I can chase a lot of electric bass guitar gear to try to sound like Victor Wooten, and maybe get sort of close - but Vic could go to any music store, pick up a $150 Ibanez, and plug it into a basic Fender combo, and start jamming... and he's still sound like Vic. (It's kind of unfair, actually.)
Compared to the electric, the upright is a very different, very physical instrument. And the sound mostly comes from the source -- most pickups for it attempt to recreate the acoustic sound of the instrument as clearly and uncolored as possible (and they all hit and miss in various ways, hence their different characters.)
Truly, the way the bass is played matters a lot - many first-timers coming from "slab" bass play the bass like it's an electric, with their fingers, and wonder why it doesn't sound like [insert random upright bass hero]. You've got to dig in, using the meaty side of your finger, and really get the string to "bloom" to get that deep, full-bodied sound.
So my suggestion would be to start with some strings that lean toward the sound you're chasing (we can help with that) and work on getting that tone acoustically first. That will be key in then being able to produce an amplified sound that is more in the ballpark of the tone you're after. So if you practice with a pickup, stop it! Concentrate on your acoustic sound, use techniques to get that big sound from the bass. You need to put a lot of meat on those strings and play to the balcony! The action at the bridge has to be high enough to allow the string to bloom without buzzing out on the fingerboard.
TL;DR: Don't look to equipment; I can't sell you a pickup to give you his sound... they can't add sustain or perform magic. That's equivalent to a vocalist ordering the microphone Sinatra used so he can sound like him. The point is to create "the sound" at the bass, using the right instrument, setup, strings, and player. Don't look to pickups, boxes, amps, etc., to produce the sound — they should deliver your acoustic sound, not make it.