Whats the difference? Nada. Use either. BUT...
FALAR or, DIZER?
if you want to impress a Brazilian do this: use DIZER in more authoritative contexts, FALAR in casual, everyday sentences. Here's what I mean:
But the bottom line is this: Use either FALAR or DIZER but favor falar for casual conversation and start adding dizer when trying to speak with more emphasis.
Examples of FALAR & DIZER in action: