I have to laugh at this. Any time there's a mention of Weatherby rifles you get Mudrunner spouting off about his "REALLY bad experience", in which he bought a rifle that was not very accurate. So he got a lemon, big freakin deal. Every company cranks out a lemon occasionally (I personally got a lemon from Cooper, but it doesn't mean their rifles suck). Weatherby rifles are significantly higher quality than the Remington SPS. I will admit that the heavy barreled Rems like the Sendero and 5Rs are a step up in quality, but those are also much heavier than the 2 guns being considered here, and double the price of the SPS. If the OP is asking about 7 lb guns I don't see much point in recommending a 9 lb gun.
The Weatherby will come with a high quality stock, very precise chamber, and a trigger that's crisp and easily tuned. The SPS gives you a plastic stock, sloppy chamber, and a trigger you'll probably want to replace. The barrel on the Wby is hand-lapped so you won't have to worry about fouling like you do on the cheap Remingtons. The Weatherby has an accuracy guarantee. These are both factory rifles but they are on opposite ends of the spectrum.
I have nothing against factory Remingtons. I own a Model Seven that I really like, but I understand it's limitations. When it shoots sub-moa I'm pleasantly surprised. With some bullets it won't shoot sub-moa and that's just life with a factory Remington. My 700 LSS performed exactly the same way until I had a decent barrel put on it.
If the goal is to reliably put 5 shots into 5" at 500 yards I think you'll need some luck to do it with the SPS. Some of them shoot well and others don't. They take more effort to find good loads for. With the Weatherby I would be confident the goal could be reached without too much effort.
While I do like Weatherby rifles I think they are a bit overpriced if you pay retail. They have a better fit and finish than the $1200 Remington heavy barreled guns, and a much better trigger, which for me puts them at about a $1600 gun.
If you drop the coin on a Weatherby you won't regret it. Look at both rifles in person if you get a chance and the differences will be pretty obvious.