I was in this predicament. Essentially, was considering the mid-spec Civic and the Mazda3 high spec(?) as they're roughly the same price. Test drove both back to back in Glenmarie where there's a Honda & Maazda showroon side by side. Here's my dua sen:
Looks: Civic looks good from the front, but fugly dead on from the rear. Overall, I think the Mazda looks better.
Build quality: Fit and finish on the Mazda is also class leading, clearly ahead of the Civic, even though the Civic is much better than the previous generation. Look at the panel gaps and the plastics in the lower parts of the cabin. That's what gives it away. I also prefer the way the Mazda's Interior looks.
Drive: This is where it comes down to preference. Handling around corners, Mazda wins hands down. It also has a much sharper throttle response. Car feels very darty, very agile, beats the Civic even when the latter is is 'S' mode. Then again, the Civic has it trumped when it comes to mid-speed acceleration. The Civic also rides better. Suspension is not as harsh and a lot more compliant on most of our Malaysian roads. In other words, the Mazda will be the more fun car to drive up Genting. But KL -> Penang on cruise control at highway speeds, Civic for the win.
NVH: Civic wins, although I should say its more a situation of Mazda losing than Honda winning. Tire roar from the higher spec Mazda3 is terrible although this may be mitigated if you get the lower spec-ed one with 16 inch shoes. Owner forums also found improvements after the swapped out the stock 18 inch tires.
Equipment levels: I'd say they're about the same. Mazda comes with all the safety stuff (ie. Lane watch etc.) and Honda has Carplay/Android auto to play with, which is nice.
Space: This one, Honda takes the cake la obviously. The rear leg room is significantly better. Downside is the Civic's rear seats don't fold down. So you might want to consider that.
FC: Shouldn't be much between them I think.
TL;DR... Mazda 3 is sportier, more fun drive. Civic is more comfy, progressive.
I settled on the Civic though. Main reason is it would be a better car for my purposes (ie. more city/highway driving vs Genting sprints). So, I would urge you to drive both and decide which you prefer in the long run.