I don't have any experience with the Weatherby but I have owned a couple Tikkas and several model 700s. I have a Tikka in 300 Win Mag and I have to say it is the most accurate hunting rifle Ive ever owned, It just shoots beautifully, I traded my tikka 22-250 on a remington sps stainless in 22-250 and it to is a great rifle. For quality and accuracy they are both great guns you should choose whichever feels and handles better for you. I have one of the original 1962 models in 7mm Mag, it shoots almost as true and has a much nicer trigger than the new factory guns despite it's many years of abuse. Personally I think its hard to beat the good ol' Model 700.