Reflecting on this more, my best guess is that you think they are similar because they are both a "grand unified theory of mathematics". To explain the difference extremely briefly then, I'd say it's a massive exaggeration to call either category theory or the Langlands program a "grand unified theory of mathematics." They each demonstrate connections between some areas of mathematics, but they are different connections, and fall very short of unifying everything. If you want to know more, I think you'd be better off learning more about category theory and the Langlands program independently of each other rather than looking for a comparison between them.