I have experience with both the 6mm Rem and the 243 Win.
The two cartridges are very close in all areas cept one.
If you plan on shooting and reloading your new rifle a lot then I would go with the 6mm Rem.
I like my 243 win just fine but the pita with it is the shoulder causes the necks to grow pretty fast so you constantly find yourself trimming the necks. Least thats been my experience.
My 243 is a Tikka M-55 and it has a 1 in 9.25 IIRC it will shoot lites out with all bullet weights cept 60 gr and below.