Hi Pete,
Such is the Audiophile Hobby. Each component has an impact on the eventual sound, and the room, your speaker/MLP positioning, your hearing ability and preferences also are involved in the end product.
The fact that your Paradigms and OMEGAs show different presentations demonstrates this well. You may find that a speaker may need to have the position and convergence adjusted on occasion, which is part of the tool-kit.
The amp qualities chart offers some general insight to guide you to the qualities the different amps/series might add.
You are correct the AMG Series is higher up the model/series chain and will impart the more refined qualities.
So yes, the the AMG STA would certainly offer a slightly improved sonic, based on the higher level of refinement.
And in some cases, the "edge" you might be hearing on the Paradigms will ameliorate over break/burn in.
Hope that helps.