I sold the big Ayre a year ago this month & the V-5x in Sept '04, so my comments are more trying to remember than recalling my latest listening session.
The V-5x & V-1x were similar but not identical and I can only guess this is due to the differences in the power supply. The V-5x has a very quiet iron core tranny (vs. toroid in V-1x & VK-200) & still has plenty of power, soundstage & all those other superlatives. Where the V-1x dominates is in the midrange while also providing tremendous power & control. I attribute that to the doubling of the power output devices per channel over the V-5x. I've felt for yrs the V-5x is a "sleeper" of sorts & wouldn't hesitate to have another V-5xe. I say that as I imagine the improvements I heard after having the V-1x made into an 'e' would be similar in the V-5x.
I like the BAT for its presentation, which I would put in the musical vs. analytical camp. Nice imaging, soundstage, etc. I suppose the two amps are similar in sound-it would be fun to do an A/B with them.
Again, I could go with either of these amps & it's just a matter of personal preference & how they sound to you. Both companies are top notch & I've been to both facilities & have had excellent dealings at both.