I've owned the BAT VK-31SE, VK-50SE and VK-51SE as well as the Audio Research Reference 3. I'm not so sure that I agree the VK-31SE was better than the 50SE. The 31SE was more dynamic and powerful, but the 50SE had a more tube like lush midrange. I would say they were different, but I wouldn't say one was better than the other.The 51SE was able to combine the best attributes of both.
That being said, I also demo'd the VK-32SE, which I did not care for, and then bought the ARC Ref 3, which I believe is still the best preamp that I have owned to date. I haven't heard the ARC LS17, so I cannot comment.
Cheers,
John