Having used a 308, 222, 6.5 x55 sweed, and a 243 a lot, and own a 6.5 creedmore. I think the 6.5 cartridge as a whole is a beautiful cartridge. At the range, the creedmoor speaks for itself, it will out compete your 243 handily. However in the deer stalking department, the 6.5 dose offer you that extra security.
The deer is a little farther, you only have a shot to go through the sholders, you want to shoot a bigger animal, etc.
I stalk mainly Sika and Red deer, and whilst a 243 as been used to hunt both successfully for a long time, once you step up into the larger stags of both, having that extra grain weight and diameter really is noticable.
especially those times where its a bit windy or rainy, and if using a 243, a 170m shot at a red stag to put it in behind the shoulder can be dicey. With the 6.5, a 147g ELDX doesnt cause me a second thought to put it through both shoulders at that range and drop it cleanly
My father used to say you can always shoot a smaller animal with a big bullet (although 95g options in 6.5 negates that slightly), you can't shoot a bigger animal with a smaller bullet.
I prefer the 6.5 as i think you can to the smaller shorter range stuff the 243 does, but gives you the freedom to be more successful and confident at the larger, longer range stuff without increasing recoil really at all.