What are the primary uses for the car? Do you have a family or often carry passengers? What are your preferences as far as handling or ride. 4 door or 2 door?
The Civic handles a bit better than the Accord. It has the same safety features as the Accord (air bags, VSA, ACE body structure, TPMS). Fuel mileage will be better. If you need a daily commuter, don't carry passengers often, and are looking to get into something around $15K or $16K, Civic would probably be your best bet. A top of the line Civic (moonroof and other features) will put you in the same ball park as an entry level Accord. The EX-L Civic with leather and NAVI will be about MSRP $21,600.
If you need the room, extra power, and ride is a priority, the Accord would probably be the better choice. The Accord LX starts around $21,000 and comes with all the "basics" (power windows, locks, A/C, etc...) and the safety features mentioned for the Civic.
Depending on your needs, if price is the main factor, I'd say go for the Civic. The VP starts under $15,000. Had I not fell in love with the Accord coupe, there's a better chance than not that I would be in a Civic Si coupe right now.
You can't go wrong with either. Which will suit you best?