First, you never stated if you were looking at the 3i or 3s. I'm going to assume you're talking about getting a 3s vs a Civic EX. The Honda has a few things missing that are standard on the 3s like leather wrapped steering wheel and fog lamps, both of which will cost you an arm and a leg to get dealer installed, which is the way Honda does options. I looked at the Civic and installation and equipment to get fog lamps installed would have cost me $655. It's a rip off.
The 3s has many options that aren't even offered on the Honda, such as High Intensity Discharge (HID) headlamps, leather seating, heated seats, and lots of accessories that can either be port installed if ordered or dealer installed like remote starting.
The interior and exterior of the 3 wins hands down against the sedan version of the Civic. The coupe version is about equal in exterior, but the interior is still horrible. Then there is the hatch option. Lots of luggage/storage space. It's not even available on the Civic.
Lastly, a drive in both reveals the more athletic nature of the 3. It simply invites you to drive in a spirited manner. The Civic is nimble, but doesn't have the same sporty character as the 3.
Think about what I've said, and go drive them both back to back before you make your decision.