I bought a Benelli 30-06 this year for my wife. She wanted a semi auto and liked it better than the BAR. I bought a box of 165 gn Core Lokts mounted the scope and have shot it at a target twice. after a couple of adjustments. I had it an inch high at a 100. I let it cool off while shooting another rifle. I loaded it up took a rest and shot 5 times.
All the shots were within an inch. I was happy. I tried it again after taking it all down and thoroughly cleaning it. And it is still on. It kicks a little more than a bolt 243.
I figure a 338 would be tamed some and would be reasonably comfortable to shoot.