AQUA all the way.
I owned both Corolla-PDM and Aqua-JDM (off course) and in my humble opinion a brief comparison is as:
Corolla if considered as good then Aqua maybe ranked as excellent and I'll score them 7.5/10 vs 9.5/10. Only thing to worry about is new vs used but JDM even if used are way better than new PDMs.
I am not sure which version of corolla is under consideration and my comparison is based on 1300cc rolla vs 1500cc which are extensively driven by undersigned.
After driving corolla for 120,0000km which includes highways too I felt Rolla lacks power and the car doesn't responds to the paddle and that is the main area of my concern. Availability of parts and maintenance is not an issue at all and the car didn't gave me a single issue during the mentioned millage except the change of entire AC unit as the compressor got ceased and though unusual but I take it as a normal wear n tear.
Aqua is a charm and the cabin is so neatly designed that you feel good as soon as you turn the power on. Seats are 3 way adjustable and you can adjust them to your comfort and can say its just like sitting on sofa vs chair of PDM cars as driver. Drive is very very smooth and it actually swallows the normal bumpy terrains.
As with all JDMs Aqua is equipped with Air bags and ABS which is another plus. Fuel average is the point which has outclassed Corrolla that is 11km/l for Corolla and 25km/l for an Aqua within city. I actually did Karachi-Dadu-Karachi (660Km run) in one tank for Just PKR 2000 with 4 passengers and trunk full.
Boot capacity though is less vs Rolla but I found its ok and you can manage to load 3 full size suitcases by compromising one passenger at back.
Only issue with Aqua is cost and availability of parts, it was really an hassle for me to get the bumper and due to non availability of new a used front bumper was purchased in PKR 23000 which is almost 4 times expensive of a Corolla but again how often your car needs it?
Owing to above I will suggest to go for an Aqua and all this is based on personal opinion.