Context: How to disable the product comparison functionality?
First of all, see how is the «Add to Compare» link implemented of a frontend product page.
As you can see, the «Add to Compare» link is not wrapped into a condition (unlike to the adjacent «Add to Wishlist» link), so there is no way to disable it generation by a backend option.
But you can do it with a CSS rule, for example:
body.catalog-product-view .product-info-main .product-addto-links a.tocompare {
display: none;
}