Should an engineer go deeper or broader?

Generally speaking, should an engineer try to go deeper (like Ilya Grigorik knowing details behind browsers and computer networks) in a particular field(s) or broader (like Steve Yegge knowing like a dozen programming languages) in many different fields?

I am amazed by both types of engineers' extraordinary abilities. If you had to choose one path, which route would you go? Or how would you weigh the importance of the two?