If you read through a lot of the posts, etc., I think you'll find listeners generally describing ARC tube gear as more "neutral" (i.e., less warm and "tubey") and the BAT gear to be somewhat darker. For me, a warm sound with lots of lower mids and bottom is the way to go. I tried an LS15 and found it entirely unsatisfactory. It lasted in my system for about 2 days, then I had it modified by Great Northern Sound. That was a signficant improvement, but then I got a BAT VK31 (not the SE), and found it to be more pleasant. But that's in accord with my own biases.
(When I hear someone describe some piece of gear as "neutral," now days the words "intolerably bright" jump into my head...though it's not always that way.)