Caveat: While I own both I have never actually got around to playing either.
As far as I can tell the rules are identical (might be the odd thing here or there, but they are basically the same).
The lite version has no artwork or photos, gets straight to business and is short and to the point. It has army lists for 30 or so forces covering East and Central Africa.
The hardback version gives longer explanations of everything with more examples and is generally more wordy. It also has period illustrations, many photos of figures and even colour plates from Osprey books. It has 80 army lists which cover the whole of Africa, rather than just the usual 'Darkest Africa' region. It also has a set of skirmish rules for big game hunting and a chapter giving historical background.
Those are the main differences, though I may have missed a few things.