Carrot Juice

[Sylvia]

Eating the whole vegetable or fruit is way healthier than juicing. By throwing out the pulp, you lose the precious fibers and the GI raises. So, what you drink is almost plain sugar.

For fruit juice, I'd definitely agree. This is probably true for carrot juice also since they generally have a higher sugar content than most veggies.
However, much of the juicing that is becoming popular now juices dark leafy green veggies which have lower sugar levels. I've seen it recommended that you start with a base veggie, like cucumber or celery, then add dark leafy greens (kale, spinach, collards, etc), then add fruit and maybe some ginger.
The recommended ratio of veggie to fruit juice is something like 80% or 90% veggie and 20% or 10% fruit juice. The fruit juice is basically there to make it palatable. The idea behind juicing is to concentrate the nutrients. It takes a lot of produce to juice, so it would be difficult to the eat the same amount of produce.

Here's a blog by a guy who is really into juicing where he describes a bit more about juicing for weight loss.