The DRV8835 is providing a higher voltage to your motor even though you are using the same power supply.
The DRV8835 uses FETs with a very low "On resistance" to switch power to the motors. Because of this, the voltage applied to the motors is very nearly the battery voltage.
This snippet from the DRV8835 datasheet shows what you can expect:
The L293D uses bipolar junction transistors in a Darlington configuration to switch power to the motors. Because of this, the voltage actually applied to the motors will be about 3 volts lower than the battery voltage.
This snippet from the L293D datasheet shows you what you can expect:
At 500mA through your motors, you would be getting a voltage drop across the DRV8835 FETs of about 0.4 volts.
Compare that to the voltage drop of about 3 volts for the L293D.
As far as I can tell from your schematics, you are using a 5 volt supply to drive the motors.
With the L293D, the motors are getting about 2 volts, maybe 2.4 volts. With the DRV8835, the motors are getting about 4.6 volts.
The current drawn by a motor goes up as the voltage increases. You are seeing about twice the current drawn for about twice the voltage - that's pretty much what I'd expect.
Since power is the product of current and voltage, the power your motor consumes will have gone up by a factor of 4 (2*V*2*A.) That's quite a bit more power than before, so the motors get quite a bit warmer than before.
To make the motors run cooler, you can try a few things:
- Insert a resistor (1 ohm or so) in series with the motors. The resistor will get hot instead of the motor.
- Use 3.3V to power the motors instead of 5V. You might not have a 3.3V source available that can deliver the needed current, though.
- Switch to motors that are intended to run at the higher voltage.
- See if they are really getting hot, or just warmer than you expected. If they aren't hotter than the motor datasheet allows, then you just live with it.
- If you are using pulse width modulation, use a lower duty cycle. With the higher voltage, you should be able to use a shorter duty cycle to get the same speed.