F4UDOA, Ki-44 never carried 20mm cannons. A lot of sources (Francillion included) are wrong on this. Of the Ki-44-II series, there were 3 major types.
Ki-44-IIa: 2x7.7mm(cowl) 2x12.7mm ,1x250kg bomb
Ki-44-IIb: 2x12.7mm(cowl) 2x40mm(Rocket Gun) ,2x110kg bombs
Ki-44-IIc: 4x12.7mm (no provisions for bombs)
Often mis-reported armaments for the Ki-44 are (2x12.7mm/2x20mm)-(4x20mm)-(2x12.7mm,2x37mm).
I think the 12.7mm were referred as somthing like "mini-cannon", which may have caused some confusion by translators. Also they used some form of HE 12.7mm ammo. This too would most likely add to the confusion of 20mm vs. 13mm

In fact, B-24 bomber crews started wearing flak helmets on flights over the CBI because the explosive content of the IJ 12.7mm shells caused "not nice" results in the bomber cockpits during head on passes.
The 40mm gun on the IIb only had an effective range of 150 meters!!!! It used caseless ammunition, so each 40mm projectile had its own propellant internally, and was expended before the "bullet" left the barrel.
Each 40mm gun carried 10 rounds!
So you only get 20 40mm shots. However, I am pretty sure if they hit it wasnt "nice".
Performance wise, well, its one of, if not the fastest climber (rivaling the J2M) as was said above. 5000m in 4 minutes, 15 seconds. It also could dive at high speeds, has the best power to wieght ratio of any IJ fighter (close rival to J2M). It was fast, could turn inside American fighters (had butterfly combat flaps too), could also outclimb any American fighter as well as out accelerate.
I believe the main problem with this fighter was its lack of range. This is probably why the IJA opted to use the poorer performing Ki-61 series for Island duty. The same would apply to the J2M. While having super performance, it lacked range for operating from islands in the Pacific.
The Ki-84 was an improvement of the Ki-44. The Ki-84 was a more "complete" fighter IMO. While it couldnt climb/accelrate as well as the Ki-44, it had much better top speed at alt, used 20mm Ho-5 cannons, and had much better RANGE!

Sorry I got to talking so much. But I love IJ interceptors.