Luckily, there is evidence that you won't lose much in terms of nutrient value when juicing. In fact, your nutrient intake from something like an apple or a carrot will increase, as the juicer extracts all the goodness from the tough plant fibers. Normally when you eat, a significant percentage of the nutrients can't be accessed by your body, as they remain trapped in the fibers. For me, juicing therefore also means getting better value for money from the fresh produce we buy!
The Department Of Agriculture tested 12 fruits and found that roughly 90% of the antioxidant activity is found in the juice, not in the left-over pulp. When you juice your intake of fruits and veggies also increases significantly. So, all in all you will get a powerful shot of nutrients, with a negligible quantity lost in the pulp.
In addition, there are research studies that shows that certain nutrients from carrots for instance, are better absorbed from the juice than from eating the whole veggie. So, this would be another benefit.
In one study the results were that, "consuming vegetable juice versus cooked or raw vegetables appears to increase serum concentrations of lutein and α-carotene"
It is also true that you only lose the insoluble fiber when you juice, while the soluble fiber is retained. The soluble fiber helps with blood sugar control, cholesterol control, etc.