Never owned one, never played one, and....don't know that I've every actually seen one in real life.
Yet, judging by how many people have played one and loved it, you'd think it was the best bass this side of the Fender Precision.
Geddy Lee
Cliff Burton and Jason Newsted
Lemmy
Chris Squire
etc.
What's so great about the Ric?
Alright, let's take these one a time ... chronologically:
1. Paul McCartney: that vid of All You Need Is Love was his first use of Rickenbacker bass (or so I read). However, he also recorded double bass on this track, so it's not just Rickenbacker. But it was a live world broadcast, so everyone saw the world's biggest pop band using a Rick bass, even if that's not quite what they were hearing.
2. Chris Squire: altered his Rick by having the neck shaved thinner (twice!) and running each pickup to its own amplifier (one a bass amp, the other a guitar amp). Once again: not a typical Rick.
3. Geddy Lee. Strongly identified with the Rick, replaced by a Fender Jazz on Moving Pictures. When asked, he replied that he could get every sound from the Fender that he got from the Rick. As it happens, this was not a typical Jazz: only the neck pickup worked, and reportedly doesn't sound typical. Furthermore he used a lot of compression.
Because of these three, a lot of bassists got Rickenbackers in the 70s, especially players who wanted a that trebly bite. The joke was that the pickup windings were only a couple times around the magnet, making less high-end loss. But few people were still seen with one when I bought mine (used) in the mid-80s.
My experience was colored by moving from a short-scale hollowbody intro-level bass from a lesser brand. So the Rick was different in every way:
-long-scale
-through-the-body neck
-better-sounding pickups
-low action
It was also rather heavier. I didn't have much choice in strings, probably Dean Markley vs Roto Sound, and would have chosen the Markleys as cheaper. I had been using a Peavey TNT 150 with a single 15" but then got a Sunn head with a 2x15" cab, and then a Fender Bassman with 4x10" -- these last two made a lovely combination, which I rarely got to use; mostly I used the Bassman alone.
Evidently the tone I preferred was well-suited to the Rick; I remember one audition where someone reached over and turned up the Low knob when I was using the Peavey, to make a more massive sound. I turned it back down, not wanting the mud. So that may be your biggest clue: the Rick could cut through subpar amplification pretty well, and no doubt through decent gear even better.
OK you say, but how about the Stingray? Well, I never had one, though I was quite impressed by how well Ben T Guy's bass filled out the sound of Snakefinger's Vestal Virgins ... a little too much, really -- but who wouldn't want to, when running bass through an 8x10" cab? A Stingray certainly offers all the sonic complexity and tone-shaping you could want -- if you wanted to -- and a Rick could never match that.
What the Rick does offer, though, that I liked: a pickup switch. One flip and bam! you got a different sound. Evidently this is not a widely-desired feature in the bass world, but I had it on that cheap starter bass, and I had it on the Rick ... and I miss it sometimes. Sure, you can do pedal EQ/boost/etc. but I didn't used to need that, and the pickup-flip meant instant change between thinner-more-bite and smoother-more-full. And the Rick did that, albeit between thinner and fuller rick sounds.
Looking for some other equivalent, I think of (what else?) the Rickenbacker guitar, and its notably jangly signature. Either you want a more bitey sound or you don't. You can, of course, tone it down (and I did) -- and I suppose you could electronically achieve the same with something else. But for me, the Rick was the bass sound I liked best -- even when its long scale meant not playing some run I might have done on shorter scale.
I no longer have it now, but make do with my ESP or Yamaha ... but when I had the Rick, people noticed it, and noticed the sound. And I do notice it, when there's some song going, and the bass has that distinctive character I can't seem to get my current instruments to do: woody, chunky, clear.