I guess that your definition of 'vintage' is going to be personal. For me, vintage has always meant a smooth, polite sound. Something that blends in to an overall mix. For this, I'm thinking my Darryl Jones with both pickups on full, and the tone control around about a quarter to a half.
For a 'solid' bass tone, I think of something thick, but well defined and punchy. It sits well in a mix, but volume control is crucial otherwise it can overwhelm a mix. For this, on a Darryl Jones, front pickup on full, bridge pickup off completely, tone on full or nearly on full.
Finally, 'modern'. For me, the definitive 'modern' sounds are Jaco Pastorius and Marcus Miller. So it's either front pickup off, bridge pickup on full, tone all the way up (jaco) or everything on full and a great deal of fiddling with the EQ section on my amp (mostly boosting a LOT of treble).
Note, please, that all of this has been done on one bass guitar, strung with the same strings. Find a good bass (ANY Lakland will do!), put some nice strings on it (I use rotosound roundwounds), and then FIDDLE. Tiny changes to the tone control on a passive bass, your pickup blend, these can make a big difference. How you play, where you pluck the string, whether you use fingerstyle, slap, or thumb the bass, all of these will have a HUGE effect. I'm not saying the pickups are unimportant - it would probably be extremely difficult to get a Marcus Miller sound out of a Hofner Violin bass, for example - but ALL Lakland basses are very flexible.
That was the whole point of the first bass Lakland made, anyway - they wanted a bass that combined all the sounds possible from a Precision, Jazz, and Stingray.
Just my two pence (yes, I'm British. what of it?!)
Cheers, SoundSupport.