more power from both sockets?

Just to gain more insight to this question, would it be advantageous to have a separate dedicated line to each component?

If your components use three pin AC plugs, that's perhaps the worst thing you could do. It only makes ground loop issues worse.

There should be no ground loop problems if multiple dedicated lines are all on the same 120V leg.

The classic ground loop is created by the AC safety ground. Or more specifically, interchassis leakage currents that are flowing through the AC safety ground.

The magnitude of the noise created by these leakage currents is a function of the impedance between the AC safety grounds of two or more components. The higher the impedance, the greater the magnitude of the noise.

The ideal condition is to have all of the components' AC safety grounds connected via the lowest possible impedance, such as plugging them all into the same outlet or outlet strip on a single AC line.

If you connect multiple components to multiple dedicated lines, the impedance between the components' AC safety grounds is dramatically increased because now they're connected via the long runs of AC wiring back to the service panel.

All of that book theory is fine, but it does not reflect real world audiophile experience. Thousands of audio enthusiasts run their systems on multiple dedicated lines -- on the same 120V leg -- with no ground loop issues. What is the person with the large audio or HT system of multiple high powered amps supposed to do ? Run everything on a single 20A circuit for fear of having a ground loop ?

I didn't say multiple dedicated lines would necessarily create a ground loop (many manufacturers isolate the signal reference ground from the chassis which is tied to the AC safety ground).

Only that they would acerbate any ground loop issues that do exist.

Your post implied that as long as they're all tied to the same 120 volt line, this would prevent ground loop issues, which simply isn't the case.