Balanced cables are best if the runs between components are long and could be subject to electrical interference which generates noise in the line. Balanced cables are able to reject the noise because the signal generated is cancelled in the opposite conductor. The connectors themselves are also much more robust and able to take more wear and tear. Musicians and stage groups use balanced XLR connectors for almost all of their hookups for these reasons. If your processor and amp are within ten feet of one another then the balanced connections probably won't provide any help. The ground loop hum is usually due to a difference in ground values between two connections. If a common good ground is used for all components then the ground loop hum issue is much less likely. Balanced connectors are also able to provide a somewhat lower noise floor because of the noise rejection and give about a 3db better signal.
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Music system
Model 990/7500/Magnepan 1.6 QRs/Technics SL1200 MK2/Aperion S-12 Subwoofer/OWA3/Sony NS75H DVD
APC H15 Power Conditioner

TV System
Large Advent Loudspeakers/ Polk center/Monoprice surrounds/Panasonic Viera 42 inch/Onkyo HT-RC260/Sony BDP S590/Directv


Home Theater System
Onkyo PR-SC886/Outlaw 7125 Klipsch RF-82 L/R,RC-62 center, RB-35 SR/SL, BENQ HT1075, Outlaw LFM1-EX/OPPO BDP-83/Directv
Harmony ONE
Blue Jeans and Monoprice interconnects
APC H15 Power Conditioner