My preference lies mainly in the fact that, according to Inside Out our emotions are running the show. In The War Within, Emotion is just one of the six main characters that govern our thought-life. He's joined by Mind, Memory, Will, Conscience, and Heart. These elements all come into play in Inside Out, but they're not the decision makers.
Also, The War Within has a fantastic faith component, which is completely missing from Inside Out.
That being said, Inside Out does have a wonderful Christ moment, and the whole film is certainly enjoyable. It also has some deep insights into who we are. It was interesting to look into various people's minds and see who was running the show: Eleven-year-old Riley, whose mind is the set for most of the main plot, is run by Joy from birth. For her mother it's Sadness. For her Father it's Anger. I'm glad we're not run by our emotions since "The heart is deceitful above all things..." But I do like the picture of choosing which emotion takes the lead.
Christians should know:
* Cartoon violence
* Anger wants to use a curse word, but, thankfully, never gets to do that