This is all just MHO, others probably have different experiences.
I don't find maps that useful, and the minis not at all. It's a problem of scale. If it's Star Wars then everything is in motion. If you have a map with squares and minis, then you're limited to the dimensions of the map and it's harder to convey a sense of motion. Very difficult to have a speeder chase over Coruscant and even attempt to use a map. Even in the bowels of a starship people are running around, hiding in rooms, crawling into ventilation shafts, etc. You couldn't possibly map it all.
Not to mention, if people (at least my players) see a grid map their instinctive response is to act tactically, and suddenly the fight becomes a grind. Dumb stuff comes up like "I move just over here so he can't reach me, because he moves X squares and that puts me X+1 away"...this is the boring detail-oriented stuff that I use this game to get away from!
If it's absolutely necessary I will draw a quick sketch on graph paper (4 squares per inch) and use pencil and eraser liberally. But I prefer (when possible) to use a piece of art/landscape rather than a map. Then they get the visuals, but don't get that tactical urge.