I've driven my 91 BRG back to back with a 2000 Boxster on the Sea to Sky Hwy north of Whistler. Other than the obvious, the main theme of the differences is - Porsche is more capable, Miata is more "fun". Another way of saying it, Porsche feels in control all the time, in the Miata you feel the speed/road/sense of danger.
Funny enough, the Boxster holds significantly more cargo.