With a few exceptions, it is preferable to consume the whole food rather than to extract part of it and drink it. Drinking fruit or carrot juice without the pulp being present to slow the absorption rate of the nutrients can spike the blood sugar and throw your blood chemistry out of balance. It is far better to consume the whole fruit. One exception is fresh-squeezed citrus fruits, since a significant portion of the pulp is generally retained with the juice. The other "exceptions" are to blend fruits such as melons, and to make smoothies out of various fruits like bananas and strawberries. Liquefying the entire fruit in a blender turns it into a juice or a thick smoothie, while keeping the entire nutritional package together. Blending whole tomato, celery and orange together makes a thick, tasty, salad dressing.
I drink OJ because it helps me get my calories in. After being on this lifestyle for a while longer, I think I'll depend on it less and less. I'm hoping to get to a point where I'll be able to eat a greater quantity of whole food.