Are you an enthusiast, or just looking for reliable transportation?
If the latter, edmunds.com and Consumer Reports are a great starting point. Definitely use the Edmunds.com method of using the internet to get dealers to bid for your business -- it has worked great for me for the last three cars I've bought.
If the former, I'd recommend also going to enthusiast websites and reading up on their forums. For example,
www.vtec.net is a great forum for general Honda info (and lots of Civic stuff in general). You'll find a lot of good & bad that you might not otherwise from reading forums.
Both cars are solid. Honda has a well-deserved reputation for reliability, and I've found that their ergonomics are some of the best in the business -- an experience I haven't had with Nissans. But I'm admittedly biased, as I now own 3 Hondas. Don't forget the Mazda 3, VW Rabbit, and Toyota Corolla for comparable in-class cars (*maybe* the Chevy Cobalt, though their quality is pretty hit-or-miss, and depreciation is horrendous). Ironically, the best car-shopping advice I've ever gotten, though, has been: don't ever buy a car you can rent at a car rental counter.
If you're an enthusiast, though, I'd recommend the Civic Si, Mazdaspeed 3, or VW GTI.