I have a Sako and a Tikka and have owned a couple of .338's in the Browning also. All excellent choices and shooters. I would caution on the Tikka in .338 if you're looking at the T3 which is quite light for that round. Buy whichever fits you best when you snap it up while wearing your hunting clothes, not just a T shirt.
And the Sako and Tikka while both owned by the same company are "NOT" the same rifles at all. Totally different stocks, actions and triggers. They share the same barrels though.