Without replacing the stock, I'd go with the Weatherby and consider the Range Certified version, given the 500 yard distance you are contemplating. If you for sure intend to replace the stock, I'd consider the Tikka instead, as the Weatherby stock and bedding strategy is part of the equation. IDK if you will see better (should) or worse (might) accuracy once you rebed the Vanguard in your new stock, but I have a strong opinion about not messing with a good thing, and so despite my success at rebedding most rifles, why tinker with something that works? The Tikka has a good reputation and the upgraded stock would be welcomed! In answer to caliber, if you are sticking to deer sized game at up to 500 yards, the 260 is going to be a better choice than the 7mm-08 because you will be sending a slipperier bullet downrange faster. It will resist drift better and provide slightly better tolerances for variances in weather and range estimation. Both cartridges you consider have the ability to humanely kill deer at 500 yards, in the hands of someone who is willing to dedicate the time to practice at these ranges. Don't let folks tell you that bullet mass is the deciding factor here (between these two specific cartridges)...energy is far more important, especially with deer sized game. My go-to tested deer load has a 100-grain 0.257 bullet leaving the muzzle just north of 3200 fps and has been shown a number of times to be a consistent one-shot kill out to 500 yards. The 7mm-08 shows some advantages at closer ranges and if you are going for elk or similar sized animals, you will be happier with the 7mm-08 and you can make it do what you need to for deer at the ranges you suggest. Both are decent choices if you are going for short-action rifle. If you move to long-action, consider the 270 Winchester or possibly the 25-06 Remington as somewhat superior cartridges.
Unsolicited, I would also strongly consider a Savage equipped with their accustock. These tend to be very accurate rifles requiring little or no modification to achieve the accuracy you are suggesting you want. You might wait a few months and see how the new Bergara B14s are faring, or go out and buy one of those and let us all know how it shoots! The potential is there with the Bergara, but it will take a little time to see how they perform for a number of shooters.
