Stale bread is traditionally made by leaving the bread out on the counter over night. It gets hard and dry because the starch crystallizes binding the H2O molecules.
The quick method of placing bread in a 225° F oven for thirty minutes drives the water out of the bread. This helps cooked dishes retain some of the breads structure and minimizes the sog factor.
So if you want to avoid soggy stuffing and pudding, use the oven method.