I can't say for sure what the differences are as I've never owned a Kitchen Sink modded amp, but I'm pretty sure the KS mod IS the BE circuit that Dave designed quite a while ago. He may have made small adjustments in the mod due to the donor amp, but I believe it's all basically all the same general BE circuit.
Any changes in snubber cap values would affect the high end and how smooth or aggressive the amp would be.
The consensus seems to be that the earlier KS mods and "Marsha" amps are brighter and more aggressive and "Plexi-like", with the first "Friedman" branded BE100 amps being a bit darker and smoother. The newer BE100 amps have been getting brighter and more aggressive again with changes to the NFB, filtering, going to Synergy caps from M150's, and the addition of the Response control.
I don't think the snubber cap values have changed in the BE100 since it became "Friedman" branded, but Dave did say in another thread here that he's recently switched from Silver Mica to Vishay ceramic for small value caps.
No idea if he's adjusted the values due to the change in cap type.
Hope that helps answer your question.