speed and quality won't change much.
That depends more on your stepper notor controllers, so if they're better, then - yep could be some improvements.
But speed and quality are more down to the actual mechanics of the printer than the electronics - in my opinion anyway.

The current popular board in the 'cheap as chips' section is the skr 1.3: https://www.youtube.com/watch?v=GNGN2iSQ5j4
The mks base is also popular. Think autowiz is using all mks base's in his machines.

The main advantage of a 32 bit board is smoothieware :-)
Probably the easiest firmware to setup and configure around.