Well, I confess to being a Tikka guy since I've bought four of them. However, the Vanguard is an excellent rifle in it's own right. I've nothing bad to say about the Weatherby.
What initially brought me to the Tikka's was the handling qualities. It just fit me a lot better than other rifles. I could bring it to the shoulder quicker, run the bolt from the shoulder, pointed more naturally, and was going to be easier to tote. That initial gun was the Whitetail version (pre T3) in 7mm Rem Mag. The T3's even improved on those handling qualities. The accuracy was initially unexpected (and an unknown), yet turned out to be gravy on the biscuit for all four rifles.
Both are fine quality rifles that will be plenty accurate for hunting (for sure) and usually plenty accurate for certain target shooting (depending on specific need).
My suggestion is to see which fits best, handles best, and cycles best if the gun is to be used in a hunting application. If a gun (any gun) doesn't fit well, it will usually not going to be shot well. Poking tiny groups off a bench should not be the only measure by which you buy a gun. Handling qualities are often an overlooked factor in favor of an extra 1/4" of group on a target. I'd say both the Tikka and Weatherby are more accurate than the shooter using them. Mine usually has more ability than me.
I love the Tikka accuracy, love the handling qualities even better. I'm a short 5'8" old man, with short arms and small hands. If I were tall and long armed the Weatherby might have been a better option.
You mileage will vary!
