They do steal each other's contents claiming them as their own, so that tends to bring out the name calling, but once someone described their relationship as 4chan being the crazy twisted internet being where as Reddit is the mellow kind one. By that I mean this:
A couple of years back, there was a news article about a little girl with cancer who was being tormented by her neighbors. During halloween, for example, the neighbor would put out tombstones with the little girls name on it all over the lawn. 4chan reacted by sending anonymous to stalk the neighbor and make her life living hell. Reddit on the other hand raised funds to donate to the girl in hopes of it helping with her cancer.
I think that story nicely describes the "big picture" of the two sites. On a daily day basis, however, they are all just jealous little virgins striving to make each other feel bad.