Sirs Honda definitely makes better engines then Toyota (generally) and ZZ series is no match with the B series Honda.
Technically comparing a JDM corolla with local one is close to non sense (unless one can justifies to compare a 1.5L with 1.8L).
Also comparing a local Corolla with local Civic is illogical and sense less untill one starts making arguments like Civic is expensive, no resale, unreliable and Corolla is TOUGH (that is really funny) or etc etc.
Buying 1.5L Axio in place of local Civic is only logical if one wants a better fit finish and sacrifice the brilliant powertrain and suspensions of Civic.
Technically speaking Toyota engines are smooth and economical but they are no match for the R18 or any performance VTEC in raw power.
Now if you pair that engine with a much brilliant chassis and body, the difference will only get larger.