I owned both up until yesterday evening (LRB and a M1A), and would have to say if shooting irons the M1A is great. Milspec doesn't mean a whole lot, the M1A will diverge from milspec much further than the LRB, which is near dead on. I quite frankly don't care about milspec however, as it's not even necessarily the best way to go about building a product. Yes, the M1A is a heavier receiver than the LRB and some feel it's stronger, it could well be, neither will fail on you in your lifetime.
Irons on the M14 are almost better than a scope, and that's the only way I shoot mine practically. They are probably the best iron sights ever put on a rifle, and the gun is built for them and doesn't accommodate scopes all that well. You have an absurd sight over bore height with a scope in an M14 unless "scout" mounted.