I think the Ruger will be better suited to PRS games than the Savage GRS. Little more barrel weight, straighter forend to sit on barricades. Nice, big port for clearing any issues (Savage has too, unlike most Rem clones).
I have Ruger Hawkeyes, have worked on a buddies Bergara and shot with it a bit, and have a couple Savages.
Relatively unique to the Ruger is controlled round feeding. CRF is an advantage for ejecting slowly to not scatter brass, but even though it’s really a push feed capable controlled round feeder, it’s really not as easy to drop one into the port of a Ruger M77 MkII action and snap over like it is with the typical push feeders used in the game. Some stages will require you to port feed, some mag failures will require you to port feed, even some stage designs where a mag reload would be allowed, but too slow, so you throw one into the port from the quiver instead of a full mag change.
Challenging for the Ruger is a proper trigger. Timney, Jard, Rifle Basix, and SpecTec all make good triggers for the M77 MkII’s and Hawkeyes, and Ernie makes spring kits for the factory triggers, but none really want to get you down under a pound. The factory trigger, as is, won’t be good for the game, flat out. Any of these options mentioned will just be OK. Correcting the sear angle and adding an Ernie spring will get you a really good trigger, but still heavier than I want in a match rifle.
Extraction can be an issue in the Savages, and feeding. I mentioned my dislike for the forend and light barrel weight for the game use. I could tolerate an accutrigger if tuned down low enough. The buttstock is a hard pass for me - that hugger hook is huge. Some guys like a hook instead of an angled stock, but I like the elevation control of an angle. I can tolerate a hook if it’s small and offers a substantial bag rider. I handled a GRS at our local Cabela’s, I don’t think it would be happy on a bag at all - I know I wouldn’t be happy with it. Also, you’ll likely see some “off-hand” stages or opportunities within stages, and the asymmetrical grip will fight you on it.
The Stealth and Stealth Evolution could be better options. The Stealth on the MDT LSS needs a longer forend, but that can be remedied easily enough with an ARCA rail/spigot. The Stealth Evolution is an option.
I would buy the Ruger Hawkeye over the Savage. RPR over the Hawkeye. And I’d think hard between the Bergara and the RPR. I walked into Cabelas to buy an RPR in 6 Creed (ended up getting one later anyway), but bought a Seekins Havak instead. It’s still a Production class rifle, but much, much closer to a competition ready rifle than these others. They just dropped a version which comes with a KRG Bravo stock/chassis, which is very suitable for the game.
All of that said as a guy who LOVES Ruger M77 MkII’s and Hawkeyes.