Corolla becomes unstable at high speed when brake is applied because of the shocks in the car.The shocks used in Honda are soft type thus when brake is applied the car`s hood can be seen bending down thus contributing to stability whereas Toyota has hard type shocks which do not allow movement with slight pressure caused by G-force
You can Practically do this by driving honda and corolla on a straight Road like in isb the new road near the parliment house.A person should stand on the side of the road to observe the car as it brakes while passing by him,
you can film it and you will have the answer yourself
Now soft shocks have a smoother drive but for our present road conditions you can feel slight bumping in car as these shocks can stabilize 2-3 sudden jerks after which the shock movement becomes de synchronized with itself to bumps plus to opposite side shock.
This problem was with old shape pak corolla but stability was good.The new corolla shocks were designed for this remedy but to their bad luck it gave rise to stability problems.Toyota Workers knows this problem but they say that they had complains in the older model that the car when loaded hits the ground, if taken on rough roads or shocks get depressed fully hitting limiter bosch on the body(THUD sound in bumps)when at high speeds thru depressions in roads thus took this step.
Soft type Shocks have a reduced life span as compared to hard type shocks
You can change the car front shocks to japanese shocks which are softer
The ABS paki corolla brakes are also improved and the complain of sluggish brakes with abs is solved