Think of it in terms of acidity and you'll find the answer just as well. Oxygen and sulfur are in the same column of the periodic table. As we descend the column our atom gets larger which means that when it bears a negative charge (ie as a result of deprotonation) the negative charge is more spread out, leading to a more stable anion. In general, the more "spread out" (or diffuse) a negative charge is the less basic our species will be. Localized charges are seen to be most basic because they are more able to "hone" in and abstract a hydrogen. All of this equates to sulfhydryls being more acidic than alchohols, and therefore sulfides are weaker bases than alkoxides.
Does that make sense?