I don’t think the BAT is automatically an upgrade. I had an original VK 3i and later a VK 30 (which I actually won in an internet contest). I honestly thought the 3i was the better of the two, but both are a little on the dark side of neutrality. I wanted something more transparent and frankly more musical (there’s that word) so I moved on.
The 3ix is a little long in the tooth and may not beat the Freya. I have seen some comparisons to some heavy hitters and it’s done very well. Don’t assume the BAT will be the winner. My guess is if your system is passive friendly, then that mode will slay the BAT.