For an extra £80, the Cali76 Compact Deluxe offers the same compression circuitry but adds more hands-on control in comparison to the non-Deluxe model.
You get a continuously variable compression ratio, plus separate attack and release knobs, which adds more flexibility in shaping the envelope.
That's not too different from the original large version, but what is new is a Dry knob (only previously seen on some of the company's limited-edition pedals) that can blend your input signal into the compressed sound for some parallel compression.
A common gripe about compression is that it affects your whole signal, taking away too much dynamic control, but by incorporating your dry signal you can have a proportional amount of your overall sound compressed. The advantageis a more natural sound but with the compressor's qualities of fattening and increasing sustain built in.