Hi JM;

All of your cartridge choices are way more than sufficient for your intended purposes.  Do you reload or do you plan to use factory ammunition?  If the latter, do you have a good local supply to draw from?  I’m recoil sensitive due to some physical limitations and much prefer the 300 short mag over the 300 win mag.  I liken the 300 WSM to a 30-06 on steroids.  I haven’t shot a 300 WSM from a Tikka platform but I have shot well over a hundred from a Kimber 8400…tolerable.  I shot one magazine of 180 gr.  factory 300 Win Mag from a Tikka Hunter and it was very unpleasant  ;D  I see an advantage with the 300 WM IF you load/shoot heavy for caliber bullets.  Personally, I feel bullet choice is more important than the head stamp. 

JM; recoil tolerance is a personal thing.  I find the 300 Win Mag to be sharp and painful as compared to the 375 H&H for example.  Please keep in mind that stock design, bullet weight, overall rifle weight and bullet velocity all skew the mix of what hurts and what doesn't (for me).  The most distasteful cartridge I've ever shot is an unbraked 340 Weatherby Mag.  The largest cartridge I have fired is a 416 Rem Mag.  Shooting the 340 Wby Mag was the closest I've ever come to getting the “Leupold kiss” from being bitten by the scope.  The older I get and the more arthritic I get 🙂 the more I appreciate standard cartridges at standard pressures. That being said, a pard of mine has a {heavy) Rem 700 300 win mag that shoots tiny bug holes with 210 gr Bergers.  It kicks no worse than any 300 WSM I've shot with 180 gr bullets…which is tolerable for a day at the bench.  Regarding accuracy, you pays your money and takes your chances.  A good friend of mine brought over a battered old Savage .308 with a vintage Redfield scope and a weathered old box of Remington 150 gr Core-lokts.  He asked that I sight it in for him.  I tried but I couldn't get that rifle to shoot over 1/2 moa at the 100 yard line.  I TRIED my best to buy that rifle…but he wanted it for a “truck” gun.  He had more expensive guns for hunting 🙂  Conversely, I know many a man who has paid big bucks for custom and semi-custom rifles who couldn't get the accuracy I experienced from that beat up old Savage.

Hi Jaegermeister, and welcome to the forum!
If I understand your preferences, you want a factory Tikka in one of the magnum calibers and you are leaning to the 300 WSM and 300 win mag.

In the Tikka line both have a 1:11 twist and shoot the same bullets with similar stabilization.  You will gain velocity with the 300 mag but won't likely be able to shoot heavier or more “vld-ish” bullets in one vs the other.  The 300 winmag has the advantage if you are using factory loaded ammo since it is widely available and you can get the ABM high performance rounds from Brian Litz, which use Berger bullets.  The 300 WSM has some advantages for the reloader in the Tikka.  Since all Tikkas are “long action” and the WSM is merely limited by the bolt stop and magazine, you can, with a few parts and no gun smithing, use a long magazine and a new bolt stop to seat long bullets like the ones you mentioned near the rifle lands.  This lets you play with seating depth for best accuracy.  If you use bullets like Barns Ttsx 180s you might find you don't need the longer seating depth, since they seem to perform well with a long “jump”.

I have used neither cartridges in a Tikka, but I see a lot of used Tikka 300 winmags for sale compared to 300 WSMs.  That may be a plus for you since you can pick up a used one and try it!

My recommendation is to research hand loading these cartridges and let your ammo interests dictate your choice.  Both will more than perform on the game you mentioned.  If I were in your position, I would consider a 6.5×55 se (but I may be biased since I would love one of those lol!