Hi,
'Twin fan' has nailed the description right !
The only things I would add are that the SMs have quite an even response across the neck, they emphasise no frequency range in particular.
This produces an almost acoustic tone when the volume is turned down.
With the pickup selector in the middle position, think B.B.King sounds.
Also SMs have an alnico II magnet by default, as compared to the Mule's alnico IV. This tends to make the bass a bit softer sounding and less focused, but also seems to give the SMs their trademark sweetness in the treble strings.
having experimented and consulted Tim, the SMs sound good in both my Les Paul and S.G. - but perfect when the SMs are in the thinner/lighter S.G. and the Mules in the Les Paul.
I feel that a Les Paul's tonal signature benefits from a slight 'mid hump' - and likewise a thinner or semi acoustic guitar lets the SMs 'breathe' wonderfully.
As Twinfan said, SMs are marginally sweeter and the Mules kick harder when you dig in.
There is indeed some lovely clean Jazzy playing and an overdriven example of the SM on the player's page, and a wealth of Mule clips.
Enjoy !
:D