In almost every depiction of Jesus, he is seen as some sort of Fabio model with flowing long hair. But James Caviezel probably should have kept his short haircut if he wanted to better portray Jesus. Not only was a short cut more in style at that time, but Paul writes against long hair (long hair was spurned by Judaism):
1Co 11:14 Does not even nature itself teach you that if a man has long hair, it is a dishonor to him?
I would say that the popular “recreated Jesus” is much more likely than the Hollywood pictures.
reality is not optional 
In the military, the short-haired Jesus would have long hair. The long-haired Jesus is a short-haired woman, especially the further back in history you go. Are you saying nobody is allowed to have hair that length? Too bad Paul didn’t specify a medium fade or this wouldn’t even be an issue. Perhaps this is all contextual and circumstantial?
Look at the Shroud of Turin…then you will know the length of Jesus’s hair.
Yeshua Bar Yosef (Joshua son of Joseph) [Jesus Christ from Iusos Christos in Greek or Iusus Christus in Latin] was the only real name he ever knew. All the other names came around 400 years later. He was indistinguishable from his disciples in the Garden of Gethsemane according to Bible Scripture. The Bible provides a description of Him. He had a short cropped beard and short cropped hair as did all the members of his tribe. Some had curly hair, His was straight. His skin was very Arab dark, almost black. By the way the letter ‘J’ did not come into use until the 1300s CE.