What is the difference? What does each do to the body?

Wholisticly speaking a low carb diet is the better option. This simply means that you get you nutrients from actually eating food & avoid carbohydrate laden foods like bread, Pasta, rice, potatoes.

The reality at least short term is that you will need Meal Replacements or at least something close to it since we simply cannot ingest enough food to satisfy our nutritional needs.

An example of a Meal Replacement is ensure or Chike shakes. Chike being the better choice because it's high protien. the biggest downfall of these is they tend to have a pretty high calorie count.

Another option is a protien supplement(shakes) and additional Vitamins & minerals.

I do the low carb, because I really don't like to eat too many processed foods. My nut encourages eating healthy nutritious food, so that what I tend to follow.