I've seen a lot of evidence that suggests they're equally healthy oils. But not all studies, some have shown coconut oil comes out ahead:
In a study in which women were fed diets with lots of coconut oil or olive oil, the coconut oil group experienced lower postprandial levels of lipoprotein A and tissue plasminogen activator antigen (1). Although postprandial effects are not always reliably extrapolated to the long term, these effects are supportive of ways coconut oil may be beneficial to risk factors of cardiovascular disease over olive oil.
In a recent meta analysis of 60 trials measuring the effect of fatty acids on cholesterol, the authors reported “Lauric acid has a more favorable effect on total:HDL cholesterol than any other fatty acid” (2). The ratio of total:HDL cholesterol is one of the strongest predictors of heart disease that I’m aware of (3). The main fatty acid in coconut oil is lauric acid. Oleic acid, the main fatty acid in olive oil, is thus not as beneficial to total:HDL ratio.
In one study (4), men were fed either lauric acid (the main fatty acid in coconut oil) or oleic acid (the main fatty acid in olive oil) via a catheter until the participants were no longer hungry. At the end of the three day trial, the men being fed lauric acid reduced their calories more than the oleic acid group. This suggests coconut oil may influence greater weight loss than olive oil.
In an old study from 1948, in rats fed coconut oil survived were largely protected from tuberculosis at a higher rate than compared to rats fed olive oil and flaxseed oil (5).
In one study, mice with gene knockouts that increase susceptibility to cardiovascular disease were used to compare coconut oil and olive oil (6). In the LDL receptor knockout group coconut oil produced less atherosclerosis.
So these studies are supportive of coconut oil over olive oil. And of course, in there are attributes like smoke point and heat stability that come into play when cooking. Coconut oil likely wins here as well, though I couldn't find much in the way of studies on this, so I'm just trusting basic chemistry. So yeah, I think both oils are good, but no convincing evidence suggest olive oil is better.
Hope this was helpful.