The most important difference is that Hotjar heatmaps are based on mouse-tracking: movements, clicks and scrolling behavior of the visitors mouse. This means that the insights you can get out of the heatmaps are limited to visitors clicking behavior. You get to know where they click most, how far people scroll and where they move with their mouse over your web page. Hotjar provides this info really clear in separate heatmaps.
An example of a Hotjar heatmap showing clicks below:
Brainsight heatmaps are based on eye tracking data. This means that insights coming from Brainsight heatmaps are limited to where people look at on your website, ad, post or video. You will learn which elements attract attention from users when they land on your page, which elements are distracting from the main flow and how much attention the CTA gets.
An example of a Brainsight eye tracking heatmap showing attention hotspots below:
Because Brainsight and Hotjar are based on different data sets and deliver different insights, they are perfectly supplementary to each other. For example, if you feel that your clicks on the main CTA are too low (as seen in Hotjar heatmaps), you can see how much attention the CTA receives with Brainsight heatmaps. And analyze which other elements might distract too much attention from the CTA. Create multiple designs, pre-test them with heatmaps again, and work towards a better converting design. Of course, post-test with the click-heatmaps from Hotjar to see if the expected effect has been realized.