Like Howard, I am also a really big fan of the 6C33B output tube. To me, in most every application I have heard it in has been a most wonderful sounding amplifier. This most certainly includes the BAT amps. For me, I think the BAT would be my heart's choice.
However, the "mind's" choice would probably go along with Albert...
The Quicksilver offers a great range of tubes you can run, which will allow you to tailor the sound a significant amount. And, both the price and long term reliability of the 6C33B put it at a disadvantage compared to what the V4 can run. Also, remember that the Quickies run twice as many output tubes which provide the double edge sword of offering double the power, but also double the cost when you go to retube compared with a two output tube per side amplifier. Though, the BAT does run a whole lot of those 6SN7s, and if you are buying prized ones, that can also get expensive.
However, the "mind's" choice would probably go along with Albert...
The Quicksilver offers a great range of tubes you can run, which will allow you to tailor the sound a significant amount. And, both the price and long term reliability of the 6C33B put it at a disadvantage compared to what the V4 can run. Also, remember that the Quickies run twice as many output tubes which provide the double edge sword of offering double the power, but also double the cost when you go to retube compared with a two output tube per side amplifier. Though, the BAT does run a whole lot of those 6SN7s, and if you are buying prized ones, that can also get expensive.