There are two separate issues.
Can you power supply (the Arduino 5v pin?) supply enough current.
Will 5v cause too much current to flow through the motor coils and damage the motor.
As far as I know there is a large voltage drop in the L293 and if so (check the datasheet) the full 5v or 3.3v will not be seen by the motor coils. In this case, that may be a good thing.
I have no idea what current those tiny motors can handle. The only way to be sure might be a destructive test.
Without knowing what current is actually flowing in the motor when the L293 is powered from 3.3v I can't answer your question about a higher voltage giving more control. That would be true if the low voltage just doesn't provide enough current. One way to test might me to see if the 3.3v works better at lower speeds. Generally stepper motors need a higher voltage for higher speed running (to overcome the inductance of the coils). That's why bigger stepper motors are driven by specialist driver boards - for example the Pololu A4988 - that have current limiting circuits.
...R