I'm especially curious as to whether the depictions varied due to the difference in status that Jesus holds between the two religions.
Also, it's not strictly within the scope of the question I asked, but I'd love to know anything about different ways Jesus was depicted in other historical periods and in various cultures at different times. If you have any interesting stories on the subject I'm interested.
To piggyback on this question with a related inquiry (if that's allowed), at some point the depiction of Jesus on the Cross changed; early depictions have 4 nails (1 in each foot), whereas later depictions and almost all modern versions only have 3 nails. My presumption is that this is symbolism of the Trinity, but I don't know for sure. Any insight into this would be much appreciated; it's bugged me for some time!
I assume, when you say "picture", you mean "what did he look like" rather than "what kind of person did they think he was like?"
So, from the 6th century, we have this picture from the St Catherine Monastery (built in the mid-6th century) by Mount Sinai. https://churchpop.com/wp-content/uploads/2015/03/6-530x1024.jpg You can see that he is clearly depicted as a bearded, long-haired man, the image we now associate with Jesus (actually, this idea of Jesus as long-haired and bearded goes back to the 4th century). However, as this was produced in Egypt when it was still heavily influenced by Greek culture, you can see that it's Greek-style, with a reasonably pale-skinned, but very dark-haired, Jesus. By the 7th century, most images of Jesus appeared somewhat like this.
As to Islamic depictions of Jesus (or Isa) this is somewhat awkward. It is fairly common in Islam to refuse to create images of sentient beings, especially holy ones. It's likely that this isn't something that developed immediately, but we don't have many sources from 7th century Arabia anyway. The Qu'ran does not describe Jesus's appearance. Generally speaking, Muslims who have depicted Jesus have either just borrowed Christian images of Jesus, as here: http://media.gettyimages.com/photos/tens-of-thousands-of-shiite-muslims-march-peacefully-with-portraits-picture-id2880655 Or they have depicted him as a generic Middle-Eastern person, with a few things to distinguish him, like riding a donkey: http://www.rawstory.com/wp-content/uploads/2015/01/0109islamart03-800x430.jpg