As a Civic owner (and ex Jazz user for a long while) it comes down to what you want.
Both come with a great mix of safety, fuel economy and features (if you chose the right spec).
What the Civic does better than the Jazz:
Power - The long gearing means you don't feel particularly fast, but it has far more grunt that any Jazz
More comfort travelling over longer distances - As a highway cruiser/repmobile the Civic is far better than the Jazz
What the Jazz does better than the Civic:
SPACE! With those foldaway seats and large bootlid, packing the Jazz is far easier than packing a Civic (which has a woefully shallow boot in sedan guise, and a better but "less awesome than Jazz" amount of space in Hatchback guise).
Town runabout - It's smaller, a bit lighter on fuel, and has more than enough grunt to get you from A to B around town. It's also good for the occasional highway bit.