can't speak for the Krell but owned the VK500 for 5 years...spacious, detailed presentation...not a hard sounding amp with power to drive almost anything.
Two totally different amps IMO. The BAT wins hands down. I have had a FPB 200 in my system and I actually own a VK200. My buddy here in town has a VK500 and owned several Krell amps. By far the best Krell was his FBP200. When he bought the VK500 he ended up selling the Krell. The newer FPB series IMO kills the KSA's. I really liked his Krell as it is very musical and smooth. Overall we both found the BAT better.
I have heard them both on my Apogee speakers. The BAT has a detailed presentation (like Larry said). The brighter side of neutral...overall a very nice amp. (I could live with it).
The Krell has a somewhat lay back sound...the softer side of neutral, (I did live with it). The Krell has more power to drive crazy speaker loads...Apogee Scintilla, Infinity Kappa come to mind.
I don't agree with (Samzx12) regarding the Krell FPB 200, although...the FPB 200 is more "BAT like" in it's presentation. So....I can understand someone liking it better.
The big Krell is old, will need rebuild, runs hot, is around 50 lbs more weight, needs a dedicated 20 amp circuit, shipping is costly, sounds best run balanced, and....needs a preamp with lots of gain to bring out it's best.
In todays world, I would probably go for the BAT over the Krell...even though, I liked the sound of the Krell better with "my speakers".