I think it's usually a best practice to try to match the type of fat to the type of food, as well as the cooking technique. For example, if you're making a stir fry, you want to use high heat and a high smoke point oil, such as peanut oil. For potatoes, I love to fry them at medium high heat in lard (not as easily absorbed in foods as other types of fat), then drain on paper towels and finish with a little fresh butter. This way you get the butter flavor without destroying it through excessive heat.
I don't fry foods very often in EVOO. I'd rather save that and use it as a finishing oil, for example, drizzling some into a pasta sauce or veggies before serving. Frying destroys its beneficial qualities.
It should also be noted that not all oils of a given type are created equal. For example, I buy an unrefined Canola oil that has a very low smoke point. It can pretty much be used only for salad dressing. I also have a semi-refined Canola that's suitable for frying.