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Some confusion is due to the fact that some of those sessions had more than one bass player. The best example is Nancy Sinatra’s These Boots Were Made For Walking. She played bass on that track, but did NOT play the famous descending bass line at the beginning. She explained in this article:
“It sure is a famous song. Jim Gordon played the drums. He was a brilliant drummer back in the day. And that’s Chuck Berghofer on double bass along with me – I’m playing electric bass.
“Chuck was asked to play the sliding part that’s pretty much the hook of the song. It took him a few passes to get it just right, where it’s more of a hesitation instead of a straight slide. I’m backing him up on the parts with a Fender Precision. People were very surprised to learn that I could get the right clicks between the notes on an electric.
“Nancy liked two basses on her songs. That might’ve come from Billy Strange, who did the arrangement. But it worked. You needed a strong bottom end on a song like this. Boy, what a hit, huh? You couldnt turn on the radio at one point without hearing ‘Boots.’”
One problem is that Carol Kaye has been very dubious in some of her claims. For example she claims to have recorded many of Motown’s Detroit-recorded hits, even though the evidence is strongly against her. Here’s a good summary of the controversy.
Bass players are kinda weird to rate. There are technically proficient ones like Les Claypool that are really good at what they do. Then there are technically proficient ones that can actually swing, like Flea, Pastorius, Bruce, Entwhistle, Wooten and JPJ.
To me, a bass player’s job depends on the kind of music being played. McCartney had some really tasty bass licks strewn throughout the Beatles catalog but his sound wasn’t over the top or in the forefront. Bass players are generally speaking supposed to lay a foundation along with the drummer in rock music. Often that means they aren’t playing anything particularly complicated nor doing much melody work.
Geddy Lee is another great bassist that plays melody lines that are stellar but they work within the context of Rush because they are a 3 piece band and have the other two great musicians helping to carry things along that work within the context of their particular brand of rock music.
I think context in this type of discussion is everything. Most rock bass players are expected to play along with the drums and stay out of the way of the lead guitarist and lead singer. That’s not always the case though. It just depends on the band.
I agree, they’re (we’re) hard to rate, but other musicians aren’t a cake walk, either.
And since there’s a lull, I would like to take this moment to mention a bass player that hasn’t been mentioned so far, and I honestly don’t remember ever hearing him mentioned in a discussion of bass players that I’ve had on the internet*: Herbie Flowers. He wrote three of my favorite bass parts, and two of them appear on the same song.
Jump Into the Fire marches and grooves at same time. That’s hard. Nevermind the fact that he goes chromatic over and over, and it still marches and grooves. My favorite Nilsson song, partly because: goddamn that’s a great bass player playing one hell of a groove.
NSFW, maybe not safe for mom…Walk on the Wild Side ups the ante by having two gorgeous bass parts. One’s an upright, walking better than 90% of us ever will, with a gorgeous fretless electric sliding away in counterpoint, just as artful and tasteful as the upright part. If you’re a bass player, and don’t at least like this song for just the bass parts, I dunno what I can talk to you about.
*Which means that someone is sure to pull up a post of mine singing his praises before I know what hit me.
Carol Kaye was definitely a big presence at a certain time. Sort of the James Jamerson of the west coast.
I normally hate these “who’s the best xxx?” threads since people nominate people I don’t like or beat me to the ones that I do. 
Besides, you can’t quantify it.
To comment on some questions upthread:
Yes, McCartney is very highly respected in the bass community.
Most basses even still are four strings tuned EADG.
The electric bass took over the music world for many reasons. It’s more portable, less fragile and can play things that don’t work on an upright. Try some Rush on a doghouse bass sometime. Lionel Hampton was an early adopter: he insisted his bass players used a Fender. They became ubiquitous. So much so, that at some gigs, I still get bass parts marked “Fender Bass”.
Jack Bruce and Felix Pappalardi.
Every bassist, I’m sure, knows about Bruce, and his bona fides speak for themselves.
Pappalardi could always go into directions that could, consistently, make a song stand out, without distracting.
McCartney could always do well, but, the only bass line of his that stands out, to me, is from Rain.
I love Rush, but, Geddy Lee’s bass playing doesn’t stand out.
Most of my favorites have been mentioned … except one: Tony Levin
Just a small taste. He ditches his prosthetic “funk fingers” about a third of the way through.
Also, killer bassline (played on a Chapman Stick) for Peter Gabriel’s I Don’t Remember.