I have found over the years that the soloed bass sound is often not the sound you need in the mix, in fact when the bass sounds great in the mix and then I solo it what you hear is crap LOL.
All my Basses are passive pickups, I do have an Ibanez that has active EQ but with passive pickups. On the basses that are completely passive I have the volume and treble full up when recording due to the fact that passive EQ controls are really only top end cut, they don't boost. The active EQ bass I have all the tone central or neutral position, I do all the EQ after tracking.
When mixing these basses I very rarely have to do massive EQ, almost never boosting always a few cuts. The exception to boosting the EQ is if I want to make the bass really stand out then I look at upper mids, but very small boosting.
I should also point out that I play the strings with fingers not pick, playing with a pick actually brings out the top end more but I prefer playing with fingers. I should say that a lot of the sound is playing technique and a good set up bass. In fact when playing live and I use a back line amp the guitar player says that every amp sounds like me or my sound LOL.
I often record DI and Amp and blend the tracks, but I also only use the amp or DI sound if that fits better, I do both so I have options, sometimes by different blending of the 2 tracks no EQ is needed.
Strings are
Elixer round wounds, light gauge
D'Addario XL Chromes, flat wounds, light gauge
My usual recording Basses:
Fender Precision 1974 (round wounds)
Fender Jazz Frettless 1994 (round wounds)
Fender Precision hollow body fretless (jazz neck, flat wounds)
Ibanez BTB455 5 String ((round wounds)
Alan.