While many dieticians recommend drinking juice, I was wondering. Wouldn't it be better to go straight to the source? Wouldn't a person actually get more nutrients by eating the fruit rather than extracting the juice from it? Especially considering much of the juice content we buy in a store is water.

One advantage of eating the fruit is that you're getting the pulp/fiber as well as the juice.
And it's usually a bit more filling.

Yes, it's significantly more beneficial to eat fruits rather than drink fruit juice. The juicing processes often eliminate many of the micro nutrients, and it's easy to drink too much juice. Most popular fruit juices are full of sugar and drinking an eight ounce glass of apple juice nets the equivalent juice of 4 -6 apples.