I have hunting rifles that have cost anywhere from $5000.00 on down, before adding mounts, rings, scope, sling swivels and sling. Every rifle you buy is a crap shoot as to wether it will shoot well or not and wether it will favor one type of ammo or bullet weight over another. I've had some very expensive custom jobs that shot very poorly and some that shot everything put through them very well. That also includes the older Tikka models. I've had the opportunity to shoot 4 different Tikka T3 rifles in 243, 6.5x55, 308W and 7-08, all of them shot into an inch or less at 100 yds and weren't at all fussy about ammunition brand or bullet weight or wether they were handloads or commercial loads. I can't say the same for the few Savages I've had the opportunity to shoot, very good to abismal. The new Remingtons and Rugers seem to be very good as well.
I would say that for the most part, the new CNC equipment being used by most of the surviveing manufacturers of firearms components pretty much ensure that you're going to get a decent shooting rifle. Remember, it was'nt all that long ago when 4 inch groups was considered to be darn good and a 2 inch group would just about guarantee a win at most club shoots.
The quality of commercial bullets made and loaded these days, after the advent of the Juenke Gage, is exceptional, especially when compared to the offerings of 20 years ago.
With modern ammunition, many of the older rifles that we considered ho hum have become exceptional shooters as well. It can't all be blamed on the firearms manufacturers.
I wouldn't feel one bit undergunned with either a Tikka T3 or a Savage, although I do have a personal preference for the Tikka offering, probably because they fit my fat little body better.
I don't know how many times that I myself or one of my hunting partners dureing the late sixties or early seventies, would sight in our rifles, usually open sights mixed with scopes that were of questionable quality, would be happy with a 4 inch group at 100 yds. The scopes always had paralax issues and if you dropped the rifle and scope together, then there was usually trouble and the scope would have to be removed and sent away for repair or trashed, even some of the old Weatherby scopes suffered from these issues. A good scope sans paralax and a good crisp trigger that surprises you every time it breaks, removeing the anticipation factor and therefore flinch, on your rifle goes a long way to tighter groups and better shot on game.
By the way, if you really want to get the accuracy bug, get into Hunter Benchrest or long range varmint shooting, talk about starting an addiction for accuracy. bearhunter