When it comes to road grip, performance, handling and comfort the Civic 06 is way better than the Corolla 09-12. We owned a 2010 Corolla for about 6 months - my Dad wanted to use it for his commute between Islamabad and Peshawar but even he grew sick of it within a few months and sold it, because it had zero grip, you never quite feel that the car is stable in your hands when you hold the wheel at high speed, whereas in the Civic you have amazing road grip and you feel quite secure and stable in high speeds.
Fuel economy is more or less similar - if you get the Civic, put the Michelin Energy Saver XM2's on your car and you'll get even better economy especially on the highways.