Hard choice between the two. I have owned a Tikka and a couple Bergaras and I honestly prefer the Bergara rifles. Tikkas have smoother actions, but the Bergara action is still pretty damn smooth. In terms of quality and feel I think the Bergaras are nicer - they have more metal on them and the factory stocks are nicer. Accuracy is a toss-up. My Tikka T3X in 6.5 Creedmoor was a 3/4 MOA gun. My uncle has a T3X CTR in 308 and I only shot it at 200 yards but I was getting 1" groups with it at 200, so it was shooting 1/2 MOA. Both of my Bergaras (B14 HMR) were half MOA guns. My brother in law just bought a B14 Ridge in 450 Bushmaster and I helped him sight it in at 100 yards and I was getting 1/2 MOA groups with that as well.
That is my experience with Tikkas and Bergaras.