The '14 Mazda 3 will come on a new platform with far superior handling, steering feel, and structural integrity than the Civic, whose platform dates back to '06. Civic is geared pretty short with a gas guzzler (for a 4 banger) motor compared to the 3. I would bet the new 3 would get a lot better MPGs compared to an Si, not just a few MPG more, but a lot, in real world driving.
Another thing to consider, the Si is getting a refresh next year, whereas the 3 is fresh. I checked insurance costs between Mazda versus Honda (CX5 vs CRV, 3 vs Civic) last year and the difference was quite a bit.
Honestly if going sedan a decently equipped 2.0 Mazda 3 Touring is pretty close in price to a base Mazda 6 Sport, which has a lot more room, comes standard with the 2.5, and looks a helluva lot better IMHO with almost the same fuel economy. Make sure you check out both. Either one, especially the 6, will be hard to find in a manual though.