Sting seems to have a keen sense of how to manipulate the harmonic and rhythmic direction of a song with his bass parts. And for that he'll always have my respect as a bassist, songwriter and arranger.
As for tone? I've been checking out some of the isolated bass parts on YouTube recently, and I've noticed something of a trend. It seems that the software that's being used to isolate these bass parts makes it possible to nail down the performance of the song. But as for the actual tone of the recorded bass track that's going into the mixdown? I get the sense that some of that sound and the overtones are being filtered out in the process. As a result some of the bass tones in these isolated bass tracks sound weak and flimsy and nothing like the rich, deep bass sounds we hear on the final mixes of these songs.
Generally speaking in the "isolated" tracks what you are hearing was either isolated from a surround sound mix for Guitar Hero, or it was from the multitrack master. While I don't go looking for these things particularly, I haven't heard any that sounded like they were created from a mixed version of a track using software (which doesn't work very well).
In some cases there are officially available snippets of these tracks that support this. For example there are documentary programs where George Martin demonstrates some of the original Beatles recordings by bringing up individual tracks on a copy of the multitrack master tape. These aren't long examples, but they suffice to give you an idea of what the track on the tape sounded like.
Bass tracks were mostly anemic by modern standards until the mid 70s when more people started to get bigger home stereos and play full albums. They had to be relatively light on the low end, they were mixing primarily for vinyl as the consumer format, and the tracks had to work well on AM radio and in juke boxes, car stereos, and portable radios, or else they might not be hits. The perception that they have great clarity and depth (and I totally agree on that) is actually partly because they don't have extended lows, and instead have a lot at 80-100 and less low end from the rest of the mix to compete with.
It's a very consistent thing that when you hear the actual unmixed tracks from classic 60s and 70s recordings that sold millions of copies, it is clear that they pretty much did the opposite of nearly every aspect of current conventional wisdom among hobbyists in the DAW age. The mics sound like they were not up on the grille cloth of the amps, there's lots of room sound, eq and compression were clearly printed to tape on a lot of them, there's background chatter and noises, it mostly sounds like it was played live with no click, and there are all kinds of playing mistakes and engineering problems like audible punchins and edits, even when great players and engineers were involved. These were not recordings that were closely scrutinized in solo mode with punch ins for all the mistakes.
The general impression is that they were working quickly and mostly concerned with the overall vibe and the sound of the mix as a whole, and willing to make tradeoffs for the desired result. This is all above and beyond the results of track bounces or track cohabitation ("we'll put the tambourine and the bass on track 2") which were due to the prevalence of 4 and 8 track machines.
It's enough to make a guy think that you are better off ignoring most generalized recording advice that you get from your friends or from places like this, other than the fundamentals of recording levels and gain staging. (I don't mean stuff like "how do you find this setting in this DAW", I use the internet for that like everybody else.)