I just typed a long post, but somehow I got logged out so this is the shorthand version (sorry).
Reduction concentrates flavors in the base liquid (wine, stock, fruit or vegetable juice, etc.), while thickening with another agent pre-maturely does not. When talking about adding a fat to thicken, I'm referring to not even combining it with a type of starch-based thickener.
Cream can be added after the base liquid is reduced, and then reduced further to thicken.
Butter needs to be added at the end ONLY, then incorporated off the heat. Never cook a sauce further after adding in the butter, or it will seperate.
Oil, as a thickener, is used mainly in uncooked sauces, or sauces where after cooking the base ingredient, you are finishing it either chilled or at room temp. Keep in mind that you need to have an acid included to bind the oil with the sauce.
Remember that sauces do NOT have to be like country-style gravy. With the exception of the oil-based method, the methods I described will never give you that ultra-thick consistency if that is what you are looking for. I prefer my sauces to be lighter in texture, even rich sauces like a demi-glace. Because the flavors are so bold and concentrated, you only need a little of the sauce to serve with the food, as opposed to smothering it with sauce that is less developed.