Most of your accuracy will be determined by the manufacturer of the rifle...the barrel being the primary provider. Even if you took 2 rifles off the assembly line that were made back to back they would most likely shoot a bit different.
That said, the chance of a real lemon is very slim, just about everything today shoots decent, so you can expect average rifles to be capable of at least MOA, with the odd gem accidentally producing half that.
So it boils down more to what you want out of the cartridge. Deer part is easy, both will bowl over deer, tons of good accurate hunting bullets available for both.
Targets, that depends on how far you plan on shooting. With a factory twist 243, you will be tapped out at 100gr SAMMI spec bullets, forget the VLD's although there are a few that may stabilize, not worth the trial and error money. 300m target shooting the 6mm is king...6mmBR , but the 243 with 87gr BTHP will have no problems, even out to 600m it will be very easy to shoot and group.
6.5cm is a little more versatile with a wider range of bullet weight selection. My personal experiences with it, i think it's ideal for the 120-130gr range of VLD type target bullets, I find it a bit lacking velocity with the 140gr+ but hey, people use them with 150gr+ and seem to think it works ok, I've found them too finicky to load myself.
With the 120-130grs 600m has also been pretty easy to shoot and group.
My top 3 target shooting rifles are in 308/243/6.5cm, all ragged hole shooters at 100m. 308 has a brake, the other 2 don't really need them, rifles are heavy enough that recoil is very mild.
The one disappointment is a 6mmCM I'm still trying to get down. Bought it specifically for the 100gr+ VLD's and it's been fighting me the whole time. Next option is going to be some Berger Hybrids for it and see how that goes. It loves the 87gr BTHP's but so does my 243, but I don't need a duplication of that.