In this thought experiment the thing to do would be to contact the manufacturer to find out what ammo they use for testing.
Then use that in all three and check the results.
My experience, chances are good it will be Federal brand, and in the most common weight for caliber.

The first answer is that all barrels are different. Their differences may -- or may not -- produce significantly different results for a given shooter.

The second and more germane answer is that all shooters are different. Sometimes way, way different. Sometimes so different that comparing results from one shooter to the next is an exercise in futility. Sometimes there is little practical difference. But unless someone always shoots from a locked-down machine rest, the shooter is part of the equation. And often the weakest link in the chain.

I'll start with a large class of bolt action rifles -- nothing special, fancy, or expensive. Run-of-the-mill commercial guns for hunting, plinking, and casual target shooting. Modern versions might have repeatable accuracy anywhere from 1 to 2.5 MOA, to moderate distances, with the right ammo. I submit that many owners of such rifles do not have consistent 1 MOA shooting fundamentals. Maybe not even 2 or 2.5 MOA fundamentals. With such accuracy variability in the rifle/ammo/shooter system, it can be challenging to determine realistic & repeatable accuracy of a given rifle. But for some gun owners in this category, gnat's-ass precision isn't really necessary, so all is fine. A little variation here and there is the rule, not the exception.

On to the seasoned competitor. Could be F-Class, High Power, PRS, steel match, or whatever. Shooters here have solid fundamentals, produce repeatable results, and exhibit sub-MOA accuracy. Maybe capable of 1/4 to 3/4 MOA accuracy on a daily basis. Such folks will use rifles carefully assembled with quality components, with quality ammo, and with accuracy capabilities maybe in the 1/4 to 1/2 MOA ballpark. Assuming there are no funky fit differences between rifles & shooters, there will almost certainly be little practical differences in precision when swapping rifles among shooters.

On the benchrest competitor. Especially the areas where the mechanical rests do almost all the heavy lifting, and the shooter is essentially there just to tap on a 2-ounce "go switch". Barrel and ammo are everything here. A rifle capable of shooting .1 MOA is good, but one shooting 1/4 MOA is bad. Barrel/rifle/ammo differences here can be clear as night and day.

Or maybe the AR15 -- an easy rifle to shoot, but a hard rifle to shoot with great precision. Put a 2-ish MOA capable shooter on the trigger, using 2-3 MOA capable 55 grain FMJ ammo, and there will be consistently inconsistent accuracy. Start with a decent barrel, a shooter with very solid fundamentals, some 69-77 grain match ammo -- the accuracy might hang with a decent bolt-action rifle, and be repeatable from one day or shooter to the next.

I've shot a lot of rifles, from run-of-the-mill commercial to custom builds. So often the talk is about what the rifle is capable of. Sometimes ammo is brought up as part of the mix. It seems that rarely is there talk about the nut behind the butt. The shooter is really the key component and the limiting factor of the rifle/ammo/sights/shooter equation.

i get completely that the person shooting is much of the precision question. But that wasn't any part of the OP's question. And what ammo got used really wasn't part of the OP's question either since he hypothesized it to be the same ammo. So we are down to the mechanical characteristics of the the hypothetical guns shot theoretically by machine rest. I'm pretty sure if the standard is "very similar" then they will. That's just the benefit of modern mfg. And that's my actual experience. But maybe others have different experience.

For these type of questions, to get an answer, actual testing may be required.

In a related scenario, I’ve seen the question about point of impact with a ‘fouled bore’ as opposed to a clean bore. As with anything, plenty of pathways should one want to go down the rabbit hole.

More specifically, I’ve tested with my Knight muzzle-loader the impact point from a clean bore, then where it may be after taking 2 shots of so. Even though I use the more forgiving(with cleaning) Blackhorn 209 powder, I’d rather keep the bore clean as long as possible.

In my example, it’s just an average 75 yard shot at a deer, nothing extreme.

Back to my testing, clean verses fouled, was almost imperceptible, 1/2” or so at 60 yards. With that amount, regular group variations likely also contributes.

We also know, certain things can work for some but not the next. Even if one fella tried it with 3 rifles, the next may have a different experience. You often see the adage, ‘works for me’ mentioned, a reminder YMMV.