The Swede is slightly larger in the case head.Bolt faces may be loose enough,but check case dimension drawings.
I'm a 257 R fan,and shoot a 257 AI.
I don't think a Texas White tail would be able to tell between them.
I've never lost a big game animal I hit with my 257.Thats not magic. Its easy to shoot a 257,or 244 well. Eyes open,no flinch.Placement is #1.
I have to agree,finding loaded 6mm or 257 R is not always easy or possible.
You can find a stash of virgin brass to work with. If you are going to pass the rifle on,A Lee hand press outfit might be able to fit in a 50 cal ammo can,or one of the Plano dry boxes. Press,manual,scale,dies,and components.
Thats one answer.Its a good one.Same ammo,every time.
Not everyone agrees with me,but not everyone has built the rifles and dealt with the problems. Everyone does seem to have an opinion,though.
Hands down,if we were talking about buying a new rifle,243,260,6,5 Creedmoor,7-08...all great choices. I don't think you can buy many 6mm/244 or 257 R rifles new today.
But you already know that fine old classic Rem will feed .244 or 6mm just fine.It was made for it. It will feed 257 R and 7x57 flawlessly. Mag box,feed rails,follower,all perfect. Barrel it and you are done.
That particular rifle was NOT made for the 243 or other 308 family cartridges.
Pull up the cartridge drawings and compare dimensions.The .308 family has a different case taper,just like the 7.62x39 and the 5.56 have different case taper. Can AR's be made to shoot 7.62x39 ammo? AK's 5.56? Yes.
But not with the same magazine geometry.
A 244 or 257 will achieve exactly the same,tight equilateral triangle stack that Mr Mauser designed his stagger box for in your Remington.
A .243 will not. Your gunsmith might fiddle with it and get it to work.Odds are good it won't be 100 % Mauser reliable.
Between 244/6mm and 257,figure on handloading and pick one. Both will be wonderful on Texas Whitetails. Its pure preference. Lone Star or Shiner..or Falstaff ? Tomatoes in your chili? Have it your way. I'm a 257 R fan.
Its not about ballistic numbers.
Its just a sweet spot.