The KOT gives a really dynamic break up, it's like a very refined blues driver, but better. There's no pronounced mids, very littly compression. Works very well with a good tube amp as you get the natural amp response on top of the pedal response, as you pick you get drive from the pedal and compression from the amp. The clean setting thickens up my Super Reverb in the midrange, makes it sound like it's louder than it is.
I use the Clone to give me a leslie type effect, although it will do some great chorus type tones, like Gilmours tones on Dark Side and Andy Summers type strat chorus with the Keeley Comp. Works very well with the KOT.
The Comp I don't use very often with the KOT - I find it destroys the interaction between the KOT and amp, but sounds great for fusion leads with the TS9 and Clone.
The Beano I use with the Marshalls, I prefer it to my Java the mids seam stronger and clearer, I'm going to sell my Java Boost following it's eviction!
The only sound I can't get with the Fender rig is the one I get with my Marshalls....deliberate that!