I have had a VTL 5.5 for a number of years, previouly had a 2.5 for a really long time, but have no experience with BAT, other than listening to friend's systems.
It may just be me, but I tube roll 12ax7's a lot in my 5.5 and can really notice changes in the mids/highs, but not so much down below 50-60Hz to me. I have noticed the lows change more when changing power cords and IC's between the 5.5 and my SS amp(McCormack DNA-500) than tubes, for me. The lows can get really dark and less tight(is there such a thing). It could be I'm tone deaf down low too? I currently am running Mullard 12AX7's and like them a lot. Why? They seem to make the mid's/high's of the acoustic and classic rock and jazz I listen to really sing. Sheryl Crow, Bonnie Raitt, Joni Mitchell and Diana Krall seem magical with Mullards and RCA clear tops, less so with Sovteks', JJ's and other Soviet stuff in mine. Changing the 12AT7's on the other hand does nothing that I can hear, either up high or down low. It could just be me too.
I hope some of that helps a little for you. Good luck and enjoy. I know I enjoy the VTL sound, but that's what I've purchased after listening, vice other good stuff, which there's plenty of.
Either way, enjoy the music and don't worry about equipment so much. Life is too short and there's too much music to listen to and wine to drink while doing it to waste too much time chasing hardware like some folks. The music is what we're after, right????