Wrinkles Away in 5 Min.

For instance, the antioxidant activity in black olives is very high. Blueberries are high in antioxidants, too. Am I better off eating both foods than concentrating on only one? Please explain how this works.

the antioxidants in different foods are certainly not the same.
the more variety of food the better.
antioxidant is refered to as anything that helps your body scavange free radicals or other "oxidants".
some antioxidants like the ones found on black olives might help the membrane of each of your cells scavange free radicals (which cause damage to cells). In the same way antioxidants like the ones found in blueberries might not have a great role in cellular membranes, but they might be great at protecting your lungs against all the pollutants in the air.
these are just 2 examples, and really there are many others I could give but without getting into too much chemistry it might be hard.
there are other antioxidants for example that help your DNA resist against things like UV damage.
for this reason, you should eat different foods and not focus on just one because you heard it is good for something.

every food has its uniqueness and will help you in a different way.