Just reading around the internet, the reasons I'm hearing for the difference in reaction between Team America from the Kim Jong Il regime and The Interview from the Kim Jong Un regime are multifold. I don't know how much of this is true, but it all sounds like it COULD explain the reasons why.
1.) Kim Jong Il actually had a sense of humor about these things and didn't feel threatened by them. Any frustration he showed was partly to put on a show so it didn't appear that he was just bending over and taking it.
2.) Despite Kim Jong Il's boasts and grandstanding, he still secretly hoped for a diplomatic resolution with the rest of the world and knew that overreacting to pointless things only made him appear more irrational and less likely to be taken seriously.
3.) Kim Jong Un is being questioned by his own advisors and the people around him. Apparently, executing his uncle for treason was a show of force to blanket the fact that there was growing sentiment against him. Basically, fear tactics to keep people from thinking about ousting him or seeing any weakness. By the same token, this is just another fear tactic to show that his rule is to be taken seriously.
4.) Because he's young and not very well versed in international politics, he believes he has to stand up to any notion of weakness to American plots. Although this is a Sony picture, it's about Americans that sneak into North Korea to assassinate him. Since that makes it propaganda, he has to overdo it in his reaction.
I am not saying these are the reasons that this is happening. It's just what I've been reading. Few people can know what is happening in his mind. It's just the most reasonable speculation of all the things I've been reading on this subject lately.