I will agree with gentleman987.
.223 isn't in the same ballpark as 30-06 un braked or .375 h&h braked. .223 from a bolt gun vs. a braked 30-06 would be kinda close. I've shot a braked 30-06, it feels like shooting a .243 with varmint rounds (as in not much).
Shooting a .375 h&h unbraked really isn't that bad. Would I really want to shoot more than 6 or 8 to sight one in off the bench? Not really, but it's definitely doable. Off hand it feels about like a 30-06 from the bench.
Brake on a 30-06? No way, not unless you're really recoil sensitive. With a .375 H&H? Maybe, but I personally would save the money for something else.