In areas where you are likely to be spending a fair amount of time aboard in inclement weather a good dodger is invaluable. I know that we would not be doing any shoulder/winter season sailing without it.
Biminis have their place in southern climes. We've sailed quite a bit in the tropics on a boat without one, and though I like the lack of visual interference with sail trim etc, at the end of a passage it's a panic to get some kind of cockpit shade in place.
I'm into the aesthetics of boats, and to me a dodger has to "look right" too. So often the dodgers are too big, to square, ill proportioned for the boat they're attached to, and this is the challenge of working with the canvas people and getting it "right" in the first place.
Our boat has a substantial bridge deck which created a real challenge for dodger height... enough space to get in and out of the companionway in a pretzel-free manner, yet not so high as to look ridiculous. The result worked well, but will keep us limber in our old age... I hope.
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)