The SOFTEST brush I have ever used had to be the Parker Chrome Handle Silvertip brush on Amazon after plenty of break in time. This was followed by a thater silvertip and finally following by the Vietnamese Kimson in tortoise. Can't comment on the BK4, but I did get my older brother a brush made from the same knot and he absolutely adores it.
The Shea Moisture brush, 10 buck range at Target, is the softest brush I have ever used. Too soft for my liking.
Part of the BK4's softness comes from its taller knot than many other silvertip brushes of similar size. A lot of the 22mmish knots have badger hair 45-50mm tall whereas the BK4's are 55mm tall.
I'd also take a look at Vie Long. Here's one of mine: http://fidosshavingbrushblog.blogspot.com/2010/05/vie-long-16510-silvertip-badger.html