SS = Thick, Vintage, with plenty of sustain. Think high-gain vintage. Fatter than both the BE & JJ to my ear. Best clean of the three. Obviously designed for modern SS tone but can accomodate many styles. Love the mids on this amp!
BE = Versatile, Hot Rod, with a bit more high-end versus the SS. Great all around modded marshall tone. More tonal options versus the SS(C45, HBE, Saturation, etc.). Designed to be a swiss army knife of modded Marshall tones. The overall voicing is damn near perfect.
JJ = Clear, Articulate, Quiet, yet can get super heavy. Heavy distortion(JBE) is very clear with a ton of sustain. Great clean channel as well. Designed to suit Jerry but does so much more, especially with the foot-switchable mod. The BE is a killer rhythm channel but has enough gain to play leads as well. JBE kicks in some low-mids and additional gain that just make the amp fucking roar.
All three share the same basic DNA. You can't miss with any of them!