The so-called brushed DC motor controller in the question is merely a dual half H-bridge IC with some inductive load protection. In other words, it is similar to the well-known L293 and L293D dual half H-bridge devices. The pin-out is simpler, providing just the pins required to drive the H-bridge and thus an attached DC motor forwards or backwards. There is no speed control, no internal PWM clock, and no logic built-in for modifying motor speed.
A brushed DC ESC on the other hand consists of not only H-bridge functionality, but also a PWM clock and PWM drive capability at the output. Thus the motor can be directly speed controlled by an ESC, without providing any external clock source or control logic.
The ESC in the question incorporates a Battery Elimination Circuit (BEC), a standard Radio Control (RC) throttle-signal input from an external RC receiver, speed control through a 2 KHz PWM, an alarm function with integrated speaker for indicating error conditions, overheating fold-back, and logic via its on-board microcontroller to gracefully handle loss of control signal in a pre-programmed manner - by throttling down the motor(s) if signal is lost for 1 second or longer.
Also, the current ratings for the specific ESC series mentioned are 20-50 Amperes, way higher than the pretty anemic L9110 H-bridge IC rated at just 800 mA.
There is no reason to expect the two devices, with their vastly different functional descriptions, to be even somewhat similar.