LL total is complete food replacement - so no other food at all. Whereas slimfast is suppost to be used in conjunction with food.
LL contains all of the vitamins/minerals/protein that you need in a day. Slimfast doesn't
They are completely different types of diet. Slimfast is a low calorie diet which helps you lose weight by reducing your calorie level. LL is a very low calorie diet (VLCD). It puts you into ketosis by reducing the calories to around 600 per day in total and keeping the carbs to less than 60g per day. This uses up your liver's glycogen store and then causes your body to use fat as its main energy source. This burns fat more quickly. In general people lose a stone a month on VLCDs.
Included in the cost of LL is group therapy using TA and CBT conselling techniques. The aim of this is to get you to evaluate your relationship with food and the intention is to change your behaviour around food so that at the end you don't put the weight back on. The are other VLCD plans which are much cheaper but none of them include therapy except for LL.