Sourdough is many types of bread. The only thing in common is that the leavening agent is natural rather than commercial yeast. You can have sourdough that isn't "sour", in fact, it's typically not sour. Ciabatta and baguettes are frequently made with natural levain (sourdough).
I think that the sour taste reputation comes from particular styles like "San Francisco sourdough" and the fact that many folks over-do it with the starter or allow the dough to rise for too long.
Try bread from some artisanal bakers, you'll very quickly experience the range of naturally leavened bread.
Do you know of a bullet-proof sourdough Ciabatta recipe? All that I've made either didn't rise, or were too weak so they spread out a lot before rising...
Ciabatta is hard. I have tried the recipe (and others) from "the perfect loaf"-- but never exactly because I don't have easy access to the flour brands he uses.
The key thing, IMHO, is high-protein (high gluten) bread flour. It helps to keep structure with any high-hydration dough. Also, if I remember correctly, ciabatta should not proof too long, or it gets too slack. I used a canvas couche and made the loaves relatively small.
I leave it on the counter overnight. I really have to work at getting any sour flavour at all. My starter smells a little like cotton candy to me though when it's ready to go, floats really well in the water.
I think that the sour taste reputation comes from particular styles like "San Francisco sourdough" and the fact that many folks over-do it with the starter or allow the dough to rise for too long.
Try bread from some artisanal bakers, you'll very quickly experience the range of naturally leavened bread.