In 34:25 the Torah says "And Shimon and Levi...went to the city and killed all the males." It appears from this Pasuk that Shimon and Levi were bad people. In Yaakov's Beracha to his children he speaks badly of Shimon and Levi. He says that they are cursed and they will be punished amongst Israel. Why, ultimately, is Shimon punished, and Levi blessed with serving God?
One possible answer is that, really, they were both punished by not having their own Shevet. However, this doesn't fully answer the question because Shevet Levi was still clearly blessed. Many great people came out from Shevet Levi, such as Moshe and Aaron also, and they are the most respected Shevet.
Therefore, I would like to suggest that which I heard from my Rabbi, Rabbi Rosenblatt. When Shimon killed, he did it out of hate, anger, and a love for killing. But Levi was different; he acted out of compassion, and love for God. This is why the Pasuk (34:7) says "because an outrage was done in Israel...such is not done". This Pasuk is talking about the rape of Dina. The reason Levi killed was because an outrage was done in Israel, the people of God, not because it was done to his sister. This shows Levi's loyalty towards God. We further see this with the Egel Hazahav. When Bnai Yisrael were worshipping the Egel Hazahav, Shevet Levi killed two thousand of the idol worshipers. Before they do this they say "Mi LaHashem Eili" whoever is for Hashem come with me. This shows why Shevet Levi received a blessing, and Shevet Shimon received a curse.