Atreus and Thyestes are definitely not the only brothers to ever go head to head in mythology.
Another example from Greek myth is Polynices and Eteocles, the sons of Oedipus, who kill each other in an argument over the throne of Thebes. Roman mythology gives us Romulus, who whacks his brother Remus in an argument over where to build Rome. Then there's Osiris, one of the key gods in Egyptian legend, who is killed and dismembered by his wicked brother, Set. And in Norse mythology, Höðr is tricked by Loki into killing his nearly invincible brother, Balder, with an arrow of mistletoe.
To the Judeo-Christian world, the most famous case of fratricide (brother killing) is probably the story of "Cain and Abel." In this tale from the book of Genesis, Cain and Abel are the sons of Adam and Eve, the first human beings. When Cain slays his younger brother Abel out of jealousy, he becomes the first murderer in history. God punishes Cain by marking him and dooming him to wander the Earth in shame. The figure of Cain now symbolizes murder in general, and his bloody tale has been spun into innumerable versions over the thousands and thousands of years it's existed. (Hey, at least he's famous.)