My bike has Force, not Rival eTap AXS. But to my understanding, the shifting mechanism is identical between Rival, Force and Red. I have only ridden 11-speed Ultegra Di2, so let me assume for a second that 12-speed Di2 is as good or perhaps a bit better.
In terms of rear shifting performance, all of them are great. You could argue about shift feel or point out that Shimano’s wired Di2 is a few milliseconds faster, but honestly, in practice, it doesn’t matter. They are all way faster than Shimano mechanical (simply the lever throw adds a whole bunch of time on Shimano’s mechanical groupsets).
I am sure you have noticed that I wrote rear shifting. That is because my current road bike is 1x. This is the first area where Shimano is behind. AXS eTap is super flexible, you can essentially mix and match all components. There are just a few exception, e. g. that you cannot use the 10-44 cassettes and up with a double in the front. You can have 1x, 2x and you have tons of chainring sizes. I can buy anything from a 38-tooth to a 54-tooth chainring (of course, your frame must fit them). I am sure third parties make bigger ones. SRAM’s rear derailleurs all have clutches, which is great, especially on 1x. Although you will benefit from that on a 2x, too.
Shimano has nothing to add here. Yes, you can get GRX, but you have far fewer first-party chainring options and their selection of gearing combos is not great. If you want 1x, you are forced to use GRX even though perhaps you want to run it on a road bike. If you live in the Netherlands, you really don’t need 2x.
Ditto with power meters. SRAM has Quarq power meters. Their spider-based power meters are the benchmark, they just work. The Rival left-sided power meter is also very good (with all the caveats that come with doubling the power numbers measured on your left leg), and most importantly, it is cheap. If memory serves, it costs $250, which is less than what 4iiii charges.
You could say “well, this is 105”. I’d reply, this is $1900 105. Not too long ago, I could almost pick up a Red mechanical groupset for that price, I think.
I would correct you on that, in terms of rear shifting you get 100 % of the performance. Whether front shifting is massively improved because of the FD, I don’t know. The only downside as I see it is weight.
Very well, easily competitive. Right now it is cheaper, more versatile and comes with a native power meter option. If you want to save some weight, you should get a Red crank, which saves about 200 g. Then you can also put a better spider-based power meter on it. (I would have gone with a Red crank, but that would have meant waiting another 2+ months for my bike — and I wasn’t going to sit out the 2021 summer riding season, because my Force crank is a few grams heavier.)
If you want to know more about Rival specifically, I think @WindWarrior has a road bike with a Rival build + Red crank. It’s a very sweet bike.