Was looking into this myself recently and deciding whether to vary my .243 for 6.5mm CM. In the end I decided to stick for the .243
Pros of .243:
Cheap factory ammo for a deer legal gun
Wide choice of round depending on quarry
Suitable for all deer in my area
Equally capable on killing foxes
Cons of .243:
Lacks a bit of knockdown power compared to the 6.5CM (probably not an issue on common Wiltshire deer species)
Not future proof for Scotland (lead ban likely, 100gr minimum bullet weight etc)
LOUD. Get a good can for your rifle
Can't speak from experience for the 6.5CM but when I was researching it looks to be a fantastic new calibre that despite naysayers probably isn't going to go anywhere. Good choice of bullet weights, great ballistics (categorically beats .308 in every way in reference to ballistics) BUT if you are planning on using it as your jack-of-all-trades rifle like I am, might be quiet expensive to go fox shooting with as a pack of 20 rounds can cost you near £40, whereas good quality rounds for the .243 (Sako for example) is £27.
If you're ONLY planning on shooting game species like deer and maybe boar if you pop over to the Forest of Dean for an evening I'd go for the 6.5, but if you want to do vermin control with it as well I'd go for .243 which is cheaper to run when shooting stuff you aren't going to eat
If you're a target shooter, 6.5 is a better round