A solo Jazz bass neck pickup sounds relatively similar to that on a Precision such that you might reliably distinguish them in an A/B test side by side, knowing there is one of each but might not without that additional information. There have been cases of old recordings where people have praised the tone as being an example of X type of bass when it was Y type. Indeed, there was quite a debate in the 90s as to which 80s Rush songs were Rickenbacker or Jazz as people were unsure, and there's more clear water in pickup design there. Put an amp in the way, maybe a touch of overdrive, and you might be hard-pressed to say.
I have a series of recordings with numerous basses - Jazz, Precision, MM, Westone from when I was thinning the herd this year. I could probably select the most similar ones from that set (slight string type differences, but all nickel wounds) and see how reliably people can tell outside a mix and in a mix.
