The Model 6's sound better with the batteries. Without going into great detail about why, they output fewer watts with the batteries, but will drive a speaker to louder levels cleanly with the batteries because A/C line noise becomes audible as the volume goes up, and none of that crap is there with the batteries. If you read Stereophile's review of the Model 2 (same amp, but the stereo version), there is a follow-up section about the batteries.
While not strictly necessary for excellent sound, the Model 6's also sound better when run balanced.
When run balanced and with batteries, I would put the Model 6's up against any solid-state other than the darTZeel. In fact, darTZeel's U.S. distributor has been known the recommend Model 6's -- or the Rowland Model 8 or 9's -- for those who cannot afford darTZeel. They retailed for almost $17k when introduced ten years ago for a reason.
Speaker cables: I had excellent results with Kimber Select KS 3033 (all-copper) and KS-3038 (all-silver) with the Salons -- the 3033's were the best value. A close friend had great success with Jena Symphony.