I have a br in a tikka595 action, super accurate and I got it dear legal with 90gr with its 24" barrel, I love it for stalking and its point and shoot with clarity and confidence made stalking a pleasure apart from its lenth,it feeds flawlessly using both a 3/5shot 22-250 mags, I now use it for longrange shooting out to 500/600 yards but running a lighter bullet.
I got a cz 243 and tidied it up added a muzzle thread with crown mod and scope, this rifle when it arrived at my Rfd was mistaken for a new rifle, but in fact had shot under 500 shots, it shoots very well and is now my dedicated stalking rifle, also used on fox's if they pop up,this also as a 24" barrel.
Recoil, far more from the 243 than the br even then the 243 is not a heavy recoil,
Accuracy, the br out shoots the cz all day long out to 200 but that's what br stands for, I home load for them both, I have used the same powder bullets and primers in both and the cz shoots superbly but the br wins hands down,
Ammo, you will find 243 ammo all over the place but the br is harder to find than you would like so home loading is the way forward IMO:
MV: the 243 will be faster than the br with the same bullet weight, but speed should never come before accuracy and that's where the slower br wins,
My overall opinion is,
They both have the ability to shoot deer/ fox and be used for longer range shots on vermin or targets at greater distances, it may appear selfish but I would and did end up with both, but if my main shooting was stalking then the 243 has to come first, if it's longer range shooing than stalking then the br is where I would head first,
What ever you choose is down to you and I hope your happy with it,after all it's you that will be using it no me
Regards
Bob