I'd always pick a map and compass but I'm kinda stubborn and fixed in my ways. As for the last question, I believe that using a map and compass gives you an better feel for the land, You pay more attention to contours, where the sun is, directions rivers and lakes drain. It sets you up to be more aware of your surroundings thus better preparing yourself mentally to handle getting out on your own.
But I did get turned around in downtown Toronto one time. No sun and no moss on the dang buildings. Now for a northerner, that was scary.