Flip-flops can get wet, Birks can't.
Flip-flops flip and flop around your feet, while Birks mold to your foot much more carefully.
Birks usually have more stuff on top to keep them on, flip-flops don't.
Flip-flops are cute and trendy, Birks are hippie-wear.  Except in Japan, where night is day.

My arch is incredibly high, so I can't wear flip-flops.  They just fall off.  But Birk-clones are no problem.