I've got an old model M-77RL Ultra Light in .250 Savage and another one that was originally a .270 Win, but I had it rebarrelled in 7x57 Mauser with a 22" barrel. In the .250 Sav. with max loaded 100gr bullets at about 3000fps, the recoil, to me, feels less than a friend's Rem Model 7 in .243 shooting 100 grainers at the same velocity. With 120gr bullets at 2800fps, the recoil is noticably more, but still what I consider to be quite light.
So if you say the .308 with, I will assume, 180gr bullets is a 10 in kick rating, I would rate the .243 with 100 gr as a 3 and the .250 Sav with 100 gr a 2 and with 120 gr a 4. You can easily find M-77RL Ultra Lights in .257 Roberts and, with factory loads, they would kick slightly less than my .250 Sav reloads. With hot handloads, the recoil should be identical because the .257 Rob Ultra Light is built on the long action and is a couple ounces heavier than the .250 Sav, and this soaks up some recoil.
The Ultra Light in 7x57 kicks about a 6 with 140gr bullets loaded around max (about 2900fps). With max loads with 160 gr bullets, it kicks about 7 to 8. I've shot a couple of Ultra Lights in .270 and they kick about identical to my 7x57.
You'll love the Ultra Light: they are very handy feeling and carry as easily as a .22 rimfire rifle.
