Puli haircuts are best described as short, medium and long coats. Short coats are those with cords that are just an inch or two long. Medium coats have cords that tend to be anywhere from a couple inches to nearly a foot. Long coats have cords that reach to the ground when the dog is stationary, and which makes the dog look like a giant fuzzy alien meteor when in motion. Ultimately, however, there is just one style regardless of length: the Puli. Each Puli cut has pros and cons.
The short-corded coat doesn't move as much. The debris may be easier to remove (and the drying period much shorter), but they tend to mat. Because there is little weight on the cords, they don't move much when the dogs walk, and as a result, they don't separate.
Medium-length dreds will happen at least once unless the dog is shaved later. This stage occurs when the puppy coat is replaced by the adult coat. This is how most of these dogs tend to be kept. Because the cords need to be trained to separate, you'll need to work on them a lot with your hands.
Then there are those amazing, long-corded, show-coat Pulis that look like a thousand pieces of varying sizes of rope exploding outward when they run. If you aren't a professional groomer, you'll most likely need one to keep a Puli's floor-length cords styled. The weight of these long dreds will help keep them separated, and it makes debris removal and dirt resistance better. There are other issues, however, such as urine odors.
Those who opt for a shaved Puli end up with a dog that looks a lot like a Poodle. It will require years for the cords to grow back. Even then, they won't look the same.