In the same weight rifles 30-06 has 20-25% more recoil than 308. And the effects of recoil is between the ears as much as anything else. Many people will swear certain cartridges recoil less than others simply because of the name. I've seen numerous internet suggestions for someone to choose 30-06 over 7mm Rem mag because anything with "Magnum" in the name will tear your shoulder off. But in this case 30-06 and 7mm Rem mag have virtually the same recoil. A 270 will recoil more than 308, but a little less than 30-06. The 35 Whelen recoils more than 300 WM and you also see people recommend it over 300 magnum.
Recoil is also cumulative. I can go to the range and shoot a few rounds of almost anything with no issues. But even with 308 I reach a point where it isn't fun anymore. The 308 is my go-to cartridge, but there are other options. For one thing the 308 you shot was one of the lighter options. A heavier rifle would have made a big difference. My lightest 308 is a 5 lb Kimber. There is a big difference in recoil compared to my 8 lb Tikka CTR.
Those choices are just fine for elk out past 400 yards. The only animal in North America I'd hesitate to hunt with those are the 1000+ lb brown bear in Alaska. And I'd still use one if it were the only rifle I had.
If you're limiting yourself to deer then look no farther than 243. If you want to hunt anything else in the lower 48 the 6.5 CM is the way to go. Recoil is between 308 and 243, but closer to 243. 7-08 is a fine cartridge, but the difference in both recoil and performance between 7-08 and 308 is indistinguishable. The 260, or for that matter 6.5X55 are good choice, but unless you already own one the 6.5 CM does everything a little better. And 6.5CM rifles and ammo are actually on shelves in stores. Going with either of the other 2 means and matching 6.5CM performance means building a custom rifle and hand loading out of spec ammo.
Recoil is also cumulative. I can go to the range and shoot a few rounds of almost anything with no issues. But even with 308 I reach a point where it isn't fun anymore. The 308 is my go-to cartridge, but there are other options. For one thing the 308 you shot was one of the lighter options. A heavier rifle would have made a big difference. My lightest 308 is a 5 lb Kimber. There is a big difference in recoil compared to my 8 lb Tikka CTR.
If you are not going to include elk the 7mm-08, 260, & 6.5 cm are fine choices.
Those choices are just fine for elk out past 400 yards. The only animal in North America I'd hesitate to hunt with those are the 1000+ lb brown bear in Alaska. And I'd still use one if it were the only rifle I had.
If you're limiting yourself to deer then look no farther than 243. If you want to hunt anything else in the lower 48 the 6.5 CM is the way to go. Recoil is between 308 and 243, but closer to 243. 7-08 is a fine cartridge, but the difference in both recoil and performance between 7-08 and 308 is indistinguishable. The 260, or for that matter 6.5X55 are good choice, but unless you already own one the 6.5 CM does everything a little better. And 6.5CM rifles and ammo are actually on shelves in stores. Going with either of the other 2 means and matching 6.5CM performance means building a custom rifle and hand loading out of spec ammo.