Are we strictly talking bolt action here?
I can make a comparison between my Tikkas and a Browning A-bolt and a Savage 116. The Browning is in 7mm-08. The action on the Browning isn't nearly as smooth. The wood stock of the browning looks better, but after having it in the field a couple of times, I realized that I was spending too much time worrying about dinging it up. When hunting I shouldn't be thinking about that at all, and that pushed me towards my first rifle with a synthetic stock (my Tikka). Synthetic stocks are just more durable and it gives the rifle a more utilitarian feel, which is something I've grown to appreciate in all things, not just rifles. At first impression, the magazine of the Browning feels much better than the Tikka. Tikkas come with a polymer magazine, which feels like cheap plastic. However, if I had to bet which one would hold up better I'd probably guess the Tikka mag. It's instinctive to think that something made of metal should be better than something made of 'plastic', but metal bends and is susceptible to weather. The polymer is likely stronger, or at least comparable to the strength of metal. Just look at the polymer p-mags that have become popular for ARs. People love them, and for good reason.
My Savage 116 is in .270. I grew up with that rifle, and I've taken most of game with it. It's very accurate. This one has a laminate wood stock, which again looks great. It seems to be a bit more durable than a regular wood stock, or maybe it just hides the scratches and dings better. The savage has a 3-position safety which I love. There is no detachable magazine, which isn't a big issue most of the time. Usually you don't need more than 4 rounds in a hunting situation, although it's nice to be able to swap out mags like you can with the Tikka (and others). Another time when it can be a pain is when you are getting in and out of vehicles periodically, which comes up in some hunting situations. The only other downside is it's just more convenient to carry ammo in a magazine than it is to carry a box of it or to carry it loose in your pocket. The bolt on the Savage is so-so, but you need to lift the handle about 90 degrees to cycle the action, which is more than it takes to lift the browning or the tikka (I think they are 60 degree). The only other disadvantage is the weight and size. It has a 26" barrel and isn't terribly heavy, but you start to feel it if you're walking around for a day. The tikka is a bit lighter, and is handier to carry around, especially in the woods.
All three rifles are great, and I'd be happy hunting with any one of them. The tikka fits me best though. Light, durable, simple, and accurate. That about sums it up.
Let me know if you have any questions. There are a lot of great options for rifles out there. You won't be disappointed in a Tikka, but there are plenty of others that won't disappoint as well. That's why you need to buy one of each