I'm going off the setup pictured on the DiveRite website (https://www.diverite.com/wp-content/uploads/2017/02/Ring1.jpg), so correct me if I'm mistaken, but..
The ring system has more parts than a loop system.
A few bits of metal, yes
The neck chokers on a loop system are simple--they just slip over the valve--whereas the stage strap on a ring system requires tools to install/remove.
Nope, Neck chokers are simply webbing loops - you just slide them over the valve
The neck chokers on a loop system are independent and don't affect the bottom leashes. You can lift a loop-system's tank by its neck choker, but if you lift a ring-system's tank by a stage strap, you can torque or dislodge the strap's bottom loop.
I don't find that at all. if climbing aboard with my tanks, I'll unclip the rears and just have them hanging from my chest rings, the weight of cylinder is supported by the choker
The top clip-in point on a loop system is adjustable. On my Hollis 100D, I've got three options (sternum strap ring, bottom shoulder D-ring, top shoulder D-ring) instead of just one ring.
I use a Stealth so I can't comment, but once the ring bungees are set I've never needed to adjust the front mount
The loop system holds my tanks up and into my armpits where I want them to be. The ring system looks dangly.
This is a disadvantage with the ring system - see end of post**
Snapping on the bungees isn't a big deal. Stick your thumb into your armpit, snag the bungee, and pull it forward across the valve handle. Boom. Done. Reverse the process after the dive.
Can you roll in to the water, into current off a boat and immediately descend?
Redundancy. If either the loop or the choker fails, the other will (literally) take up the slack.
As long as my bungee is okay there's nothing to fail- basic pre use kit inspection mitigates that.
** So the primary advantage of the ring system is that yoru cylinders are directly attached to your webbing via load bearing metal components and it's incredibly easy to clip on the cylinders on a boat, and jump in with no time spent on surface attaching loops etc
Same with walking around a boat with tanks (AL 80 in my case) I've gone of small ribs, clipped the tanks while sitting on the tube, or backrolled off slightly bigger boats. Sometimes one boat requires a giant stride of 8' from the side.
Generally also I've also got a scooter in my hand with it's leash attached.
I adopted ring bungees because it meant I could optimise my rig for my diving - open ocean generally on to site with significant currents, the prime consideration that it should be as time efficient as a BM with large steel and slung AL40. If the system required surface faff then it would be a no go. If you're swept off the site, the boat needs to collect you and re drop you which is a major hassle
All that said, it's not perfect. As you pointed out the tanks don't get pulled in as snugly as loop bungee but since I'm not in a cave, its not an issue. It certainly hasn't been on wreck penetrations.
But with every system whether on SM or BM etc there are always compromises and I feel the trick is to adopt or optimise a configuration that best meets the requirements of the environment. I'd never suggest that there is one perfect system for all, because there isn't - I just like to offer alternatives since its always worth considering different solutions