Which bypass cap position creates a cleaner voltage and current feedback circuit?
In a word - yes. The purpose of the bypass capacitor is to keep the voltage across the load stable by providing a local energy store which can satisfy AC current demands without causing ripple in the voltage across the load. Since V=IR, the higher the resistance between the bypass capacitor and the load, the higher the ripple voltage that will develop across the load.

Moving the capacitor closer to the load (as shown in the right hand side of the diagram) means that current supplied by the capacitor will not have to flow through the current sense resistor, and hence less ripple voltage will be observed. Depending on the amount of ripple you're talking about here, you should be able to easily observe this with an AC-coupled scope probe across the load.