A good UI UX design agency is one that creates a memorable experience, while intuitively working towards a central digital goal. Quantitative data on site usage is a very important metric for a UI UX design company, as it helps understand the target audience, focus areas and most performed actions on a page.
Eye tracking, tagging elements with UI trackers, heatmaps, are all tools that help design a better UI/UX product. There are also specifics that a UX firm uses - where a particular element is examined in great detail - like say a button or a one click checkout, and analysis of if it has been effective. A great deal goes into Ui/UX design beyond just design.