I currently own 3 wood stocked Steyrs, (270 Win, 6.5 x 55 & 7mm-08). Have owned five Steyr Mountain/Pro synthetic stocked rifles, (308 Mountain and 300 Win mag chrome moly bbl & action, the stainless pro hunters in 260 Rem, 7Mag, 376 Steyr,) All have two stage triggers and the safe bolt system. The 6.5 x 55 Classic Mannlicher has a set trigger.
I own four of the Ruger Americans, (22 Mag, 223 Rem, 6mm Creedmoor, 6.5 Creedmoor) My favorite of these is the 22 mag. I often take it along with me if I'm sitting in a stand and snipe targets of opportunity! Its an amazingly accurate piece of work. First time I took it out was at the 2016 Campfire hog hunt. I'd killed my max allotment of hogs the first morning so, it was varmints from there on. I nailed 4 cow-birds with 4 shots between 50 and 80 yds. 100%.
I own no Tikkas, but have owned over 2 dozen Sakos in various iterations.
All of the aforementioned rifles were purchased pre-enjoyed except the 376 Steyr which I bought new at Euro-Optic IIRC. The RAR's have the lowest price point, all under $400. I don't follow Tikka, so I'm not good there. I've paid between $475 and $750 (new 376 Steyr Pro Hunter) for the Steyr synthetic rifles. IMHO, at those price points you will most likely not make much coin if you decide to sell. I much prefer being able to buy, keep a while, shoot and sell for a profit. Helps finance the addiction.
So, with that in mind.
Out of the box accuracy. You do not state whether you will be using factory ammo or your own handloads. I've not shot factory fodder out of any of the aforementioned rifles except for the Steyr in 6.5 x 55 and the 7 Rem Mag The 6.5 came with five boxes of Norma Oryx 156 grain soft point Ammo. I had several boxes of 160 gr. Partitions given me, and they shot well. To date I've not sat at the bench and shot past 200 yds. using any of these rifles. At 100 yds, IMHO for all hunting purposes, under an inch is sufficient and to me first shot out of a cold barrel tells all. I've been extremely impressed with the Steyrs. While at the range on several occasions I've had guys next to me shooting TIKKA's, and IIRC, when they brought back their targets after they retrieved them, were all smiles.
I would bet that the biggest difference would be fit, finish and function, with the Steyr first, Tikka, second and the RAR, third. You can read reviews by googling "X vs. Y " or "X vs. Z", so I won't get into specifics as to action lengths, weights, barrels and lengths, twist rates etc. To me the Steyrs are so butt ugly that they appeal to me. The stock length on the Mountain and Pro Hunter editions are adjustable. I do like the Safe Bolt system and the rotating 3 position Tang safety that locks the bolt on the Steyr vs the RAR two position tang safety. Others may like the on/off of the RAR. Both have a cocking indicator, which I like. I prefer the Steyr Mag to the RAR. The RAR comes with a scope rail mounted, you will have to spring extra for the Steyr rings (and about $500 extra if you want the Recknagel Twist-off mounts)
I usually tote wood stocked rifles when its not raining.
Here are the three Steyrs I tend to reach for in bad weather.
Steyr Pro Hunter, 7Mag
Steyr Mountain, 308 Win.
Steyr Pro Hunter, 376 Steyr.
You mention the 308 Winchester. My Steyr Mountain rifle in 308 Winchester came with both a 5 round and 10 round magazine. I use the 5 round exclusively. I like the flush mount as I usually shoot off shooting stix, or some type of rest. Both the RAR and the Steyr Mags fit flush. I prefer the Steyr mag vs. the Ruger Mag.
With the 20" barrel, this combo in 308 Win. works great for thumping hogs after dark, and the first subtension on the little Burris scope lines up perfectly at 200 yds with my 150 gr. Accubond loads.
I will say that when the weather is nasty out, and I don't want to track of an evening. The 376 Steyr has become my go to hoglet thumper as opposed to my Nosler Custom Sporter in 325 WSM.
This from the 2016 Campfire Hog Hunt. I shot four in quick succession. At this time I did not realize the limit was four hogs for the weekend. I would have shot more but I only took six bullets. A couple of the hogs were on the run and I missed once and put two into another.
and if it looks like shots are gonna be 200 yds plus in the rain, its the Pro in 7 Mag I reach for if not my Rem 700 KS in 300 H & H.
and, being as they are one of the best kept secrets in "show-biz" you will not see many in deer camp, (at least in Texas,) anyhwo
So, IMHO,
Steyr!
BTW,
my latest Steyr............
Custom Mannlicher,6.5 x 55, set trigger, Recknagel twist-off mounts.
ya!
GWB