I've only heard the BAT tube gear. It is marvelous gear. Very well built. The sound is superb, very quiet for tube gear. I could easily live with it. But, I made the change to Ayre because I listen ALL the time to either the radio or discs and felt bad about running tubes all the time. The Ayre SS gear is easily the best SS gear I've experienced. I think there is something special about the no feedback designs (BAT SS does this as well). Compared to the BAT tube gear the Ayre is faster, more controlled, and more transparent. But, it is leaner in the midrange, more analytical. If all I listened to was jazz vocals and chamber music I might prefer the BAT. But, I like big orchestral stuff and I think the Ayre wins out due to the control and low distortion. Your milage may vary....
BTW - I have Avalon Ascendant speakers and Cardas Golden Reference speaker cables and Ayre Signature (Cardas) balanced interconnects. Cardas Power Cords