I can say from ALL of my testing comparing multiple recordings of the same bass, strings, player, and midi accompaniment tracks that there is no discernable difference outside of pseudoacoustics.
I have done the recorded A/B testing with several of my custom built (homebrew from rough lumber and also Warmoth assemble) basses - and nobody has been able to accurately and continuously determine which stringing method was used when listening to recorded playbacks. this is true for P-bass, J-bass, and SCPB type pickups (Nordstrand and Barts) ... is true for the bass track in context and heard solo ... is true regardless of the body wood, music style, playing style, fretted or fretless, 34" or 35" scale
while someone may want to hear a difference because they've been conditioned to expect a sonic difference, there is no difference in sound on a properly constructed instrument IME and IMO
the caveat to this is that a taper core string will sound different due to its core resting on the bridge saddle when top loaded and its wrap resting on the bridge saddle when thru-body loaded ... but since all things aren't truly equal in this specific scenario, it isn't an apples/apples comparison is it? it is also what Mike Watt experienced (and incorrectly attributed) when using the spacers on his top loader - he also used taper core strings, and the spacer put the string wrap onto the saddle instead of the string core
all the best,
R