How well they kept their hair would depend a lot on who you asked. It was probably not exactly better kempt than a dog's hair for either H. sapiens or H. s. neanderthalensis, but neanderthalensis had more of it. It's not as if either of them were totally unhygienic, though; they probably spent quite a lot of time grooming eachother, if other great apes and some human cultures that have no qualms with physical contact are anything to go by.
They probably would have been pretty shaggy. But on the other hand, reconstructions are quite expensive, so there may be the motive of giving the public what they want: a picture of a hairy, unwashed caveman.