Hate to say it...

But my first impression, given the info you present, is...practice my friend, practice.

The H&R "accuracy" is par for the course, IMHO.

On the Omega...

First, 150 grains of anything is overkill, IMHO.

Second, are you being absolutely consistant with your measurement of the charge weight?

Third, are you being absolutely consistant with how much you compress the load?

Fourth, with both firearms, trigger pull quality, is it there or not?

Fifth, with both firearms, sandbags from a solid bench? Screws tight? sling swivels dragging on recoil? Calm wind?

Lottsa things can mess up "accuracy"............