Will the 300 be a better rifle? So...

Are you asking if the Tikka is a better rifle than the Ruger Hawkeye?

OR...

Are you asking if the 300win mag is a better cartridge than the 30-06?

The Tikka isn't a better rifle, in my opinion. Not really worse, but not better either.

The 300win mag isn't a better cartridge really either. Not really worse either, but not really better - especially if you're shooting factory ammo. With 150-180grn pills in most factory loads, you won't see any more than a 100-150yrd difference between the two, and that gap only really starts to matter after 1,000yrds.

So for my money, I'd look at more ammo, better scope, or hunting tags, rather than another rifle.

Unless, of course, you just want another rifle...