We bought a mazda3 over a civic, only because mazda offered better trade in and my wife likes the look more. Comparing base to base model though, i think civic is a better buy, though it also depends on which dealer is more willing to give discount. The updated 3 now is better value with a few extras.
I think the 3 may have better road holding and a sportier drive, but very nosiy front suspension, the 4 speed auto is not the best, and the fuel consumption could be better for a small car. The Civic on the other hand rides smmothly, has good interior space, good fuel consumption, but too soft/not sporty/youthful as it once was, limited and boring colour choices, and the paint does not have the lustre of others, eg euro. Just what i think.