Coconut pure oil or extra virgin olive oil?

Well, I have a medical issue (familial hypercholesterolemia) which makes it prudent for me to watch my intake of saturated fat. While plant sat fats are supposedly less of a concern than animal saturated fats, I tend to err on the side of caution in regards to the issue and just avoid it.

Saying that, for most people, this isn't a concern, especially if you're watching calories and regulating your intake of oils so that they're not ridiculously excessive (causing obesity). If you're eating a healthy amount of saturated fat (not too much), the choice between olive and coconut oil comes down to preference, really.

In some cooking applications, one is preferable to the other due to the flavor it imparts to the dish. That's pretty much it.

There are a couple good articles on this. The new one by the New York Times (December 22, 2017) and this article about the smoke point of different cooking oils (the point their nutritional value is broken down). The later article was updated December 6, 2017.

Most articles seem to think the olive oil is better if you are worried about cholesterol. I think a lot of people started using coconut oil because it has antioxidant properties. If you use coconut oil it's better to make sure you get virgin coconut oil as some believe the more gentle processing of the oil keeps the greater saturated fat from being as harmful as many people would paint a picture of it being. I'm pretty sure that means if you're buying the coconut oil in a bottle that looks like every other cooking oil, you're buying an overly processed coconut oil. I've always used the extra virgin coconut oil you have to melt in the pan.

Back when I was still frying things my cholesterol never went up and I used coconut oil all the time. That could just be good genetics. These days it is harder to tell which articles on the internet are true and which are prompted by some lobbying group. When actual studies are done, it appears the higher saturated fat of coconut oil isn't as deadly as olive oil proponents would like people to believe. If you eat healthy food, try your own test. Use olive oil one month and coconut oil the next. If you're in tune with your body it will let you know which it prefers and blood tests will show you any trends your cholesterol count is taking.