There are many juicers out there and not any one juicer is best at juicing everything. I am specifically interested in juicing leafy greens and vegetables like carrots.
Hydraulic press juices such as the Norwalk first grind the produce into a pulp, then press the juice out of the pulp. The theory is that malic acid in green apple pulp can release more vitamins and minerals from the other vegetables and fruit. The hydraulic press action squeezes more juice out than other types of juicers. But you're looking at $2500 for a Norwalk.
Macerating juicers would be next, up around the $400+ mark. Gear crushing action, leafy vegetables no problem. Not as much juice extraction as the hydraulic press machines.
Then would come auger style juicers, they easily handle leafy vegetables and wheatgrass, but give a little less juice than the macerating juicers.
Finally the cheapest powered juicers, the centrifugal juicers. I've had trouble using them for leafy greens as there are not solid enough to be forced chopping blades. Usually more solid vegetables are required to follow them to force them through.
Here's a paragraph from the popular Breville centrifugal juicer seen in the movie Fat, Sick and Nearly Dead:
Carrots are fine in all the juicers.
Champion-type macerating juicers work great on carrots; the teeth take them right apart, getting out all the juice and leaving behind a dry pulp. I've seen mixed reports on how well they work on leafy greens.