I agree, having both, the BAT is more dynamic, while the CJ is more soft and lush.
I prefer the CJ for smooth jazz fusion and classical piano, I use it with a CJ pre-amp and smaller speakers. The BAT is best for big dynamic and a large sound stage, such as a symphony, or a great modern pop sound and vocals.
My BAT amps were several; from the BAT 60, to now, having two VK 55 factory set to mono. They test out at 118 watts onto 4 ohms. I use them in a large line source speaker, much like the old Infinity IRS, for mid-range and high frequencies, with ribbons. The pre-amp is the ARC, now using an LS 16 and all balanced interconnects, later LS 15 is about the same and I like traditional tubes, from my pre-amp, to the 'super tubes' used for gain drivers on the VK 55.
For me, they are two different philosophies, form traditional Fisher sounding old tubes, where CJ has the closer sound, much like the older McIntosh and Marantz; even the older ARC power amps have this softer more rounded sound.
The BAT is at the other end, like the newer VTL, the newer Cary too. ARC, the later LS models, somewhere, in the middle, more lush than Sonic Frontiers, and more palpable than BAT pre-amps sound to me. huh?
Also, the BAT is wired in triode, while the ARC are tetrode, thus to make a VT 100 series ARC triode, you end up with 50 watts, so consider, after the big VTL signature amps, which are switchable and very powerful, BAT is a great choice. Of course, it you are super rich you can have a VAC mono 140 watts, pure class A, with 300B tubes :)
I would say if you like the older tube sound, go for CJ, but use and all tube pre-amp, like ARC model 6, or 8, or McIntosh model 11, 20, 22, or an old Marantz, if you are carefree of cost, as I think the Sun Valley Marantz are more collectors items today.