Why not Google Analytics "overlay" report?
Google Analytics "overlay" report is based on URLs users visit, not the coordinates they actually click. If a user clicks an image that has no link on it - you don't see this click in GA.
Similar - if a page has two links that point to the same URL, and the user clicks ONE of them - Google Analytics will show two clicks on the "overlay" heatmap. Because it can't tell which particular element was clicked.
Now, click heat maps
On the contrary - a heatmap analytics tool can track the users mouse cursors and the exact coordinates where they click. Who knows, may be your visitors are trying to click something that's not even a button? You want to know that.