As the others said, .308/.30-06 generally seems to have less recoil. However, shotgun shooting doesn't have the long anticipation of sitting at a bench, slowly pulling the trigger to really focus your mind on the recoil that's about to hit your shoulder.
I took my 12 gauge double, a rather light weight field gun, to the range once to see how it shot with foster slugs...
THAT woke me up!
I was shooting over the seat of my motorcycle at 50 yards (we didn't have a 50 yard range at the time) and not at a bench, thank God. I was pointing 12 o'clock after every shot!
My little .308 is NOTHIN' compared to that. It's a very light rifle, but I can shoot it all day long, no recoil pad and a T shirt, and it doesn't bother me. I am rather recoil tolerant, though, fired up to .375 off the bench, but still, it feels little more than my .257 Roberts to me. OTOH, my much heavier Savage 110 in 7 mag is a definite step up the recoil ladder. That one has some smack to it. I usually put on a Past pad to shoot that thing from a bench if I'm going to put many rounds through it.
You can expect bargain basement performance from a bargain basement rifle such as Rem 710. Sometimes it pays to spend a little more for good quality.
I've never priced the 710, ain't interested, but I don't think you'd spend a lot more for a 700 ADL or a Savage 110, two guns I have or do own that I can say are quite good. The Savage has to be THE bargain in rifles. Mine's an older gun without the Accutrigger and it's still excellent. I tuned its trigger to about 3 lbs and it shoots 1 MOA with a couple of hunting loads. That's all I can ask of a hunting rifle.
I prefer my Remingtons to the Savage, more refined rifles, look better, finished and fit better, but they don't honestly shoot much better. For the money, the Savage is a deal. That Tikka might be a more refined gun as is the 700 Remington, but I doubt it shoots any better.
Whatever you do, though, stay away from that 710. I've never heard anyone praise that thing. I've never handled one, but it sounds like a POS from everyone I know that has.