Recoil from a 7.5 lb rifle. These are my actual loads calculated with an online recoil calculator.
6.5 Creedmoor/143gr ELD-X @ 2650 fps 12 ft lbs recoil
308/178 gr ELD-X @ 2620 fps 18 ft lbs recoil
I don't own a 243, but typical recoil is around 10-11 ft lbs.
30-06 will be in the 20-22 ft lbs range.
With 150 gr loads a 308 will be around 15 ft lbs recoil, but the 178's are a more fair comparison since the BC's and on game performance are closer.
The difference in there, but it may not be as noticeable as the numbers show. Most people can't tell any difference until they see 4-5 more ft lbs difference. The 308 isn't really considered a hard recoiling rifle and I'm sure a lot of people couldn't tell the difference between a 140 gr 6.5 load and a 150 gr 308 load. Most people don't have much issue with recoil until they get over 20 ft lbs.
At least for a few rounds. If you start shooting 50 or more rounds in one session even small differences in recoil start becoming more noticeable.
I like the 6.5 a lot, but other than recoil there isn't much difference until you get out to about 600-700 yards. After that the 6.5 starts pulling away.
But the 6.5 is enough better that it is the cartridge of the future. The 308 will never go away, but will gradually be surpassed by the 6.5 Creedmoor. Even the military Special Forces are moving that way
http://soldiersystems.net/2018/03/23/ussocom-adopts-6-5-cm/