There is a fairly good description on the Suzuki Allgrip microsite.

http://www.globalsuzuki.com/allgrip/

I haven't had the real need to take my Vitara out of Auto yet. I did try out Sport mode on my test drive and it really made a difference to the performance.

 

The auto is similar to your Vauxhall, snow/mud changes the power applied to each wheel based on sensors that determine slip and etc, so the ratio of power is varying according to need, and lock just locks the split 50/50 all the time. There are arguments as to why the snow/mud mode is better in those conditions than a lock mode.. but there are also arguments against it.. 50/50 is usually for the worst situations though.. As driving on snowy roads for example doesn't necessarily need the most aggressive option running constantly... In fact it is probably better to let the computer(s) figure out which wheel needs more power (to prevent spinouts.. unless you're beeig a hoot )

 

I haven't used the snow or lock modes yet, but the sport mode is amazing. Just turn the dial clockwise and it clicks in instantly. Then the fun begins: Suspensions tightens, the throttle response sharpens to allow longer times between changes, and the power settings seem to change allowing faster than normal acceleration. It will easily top 200 kph, so it transforms to sports car performance in a SUV body.
I confidently predict that once the public get to hear about this little car, sales will soar.
It's really is that much fun.

Max