Welcome to PhilSE. Are the categories emotional and rational "real", and do they have an empirical basis?
What Is Reality Anyway?
The first part is a very broad question, because reality itself may be an essentially contested concept. From WP:
Walter Bryce Gallie (1912–1998) introduced the term essentially contested concept to facilitate an understanding of the different applications or interpretations of the sorts of abstract, qualitative, and evaluative notions2—such as "art", "philanthropy",3 "power",4 and "social justice"—used in the domains of aesthetics, sustainable development, political philosophy, philosophy of history, and philosophy of religion.
When one talks of what reality is, one can see the idea thoroughly tied up in the politics of being and thinking to such an extent, that detached from reality might even serve as a legal basis for committing someone to an institution. Reality is often, therefore, a function of one's worldview. Of course, one popular worldview is that there is only one fundamental reality and that "science" determines it. This is a mild form of scientism. In this sense, one can easily clarify by using terms as "personal reality" and "physical reality" to observe that reality can only be perceived through a subjective lens ultimately.
But for most people who don't split hairs, the categories of "emotions" and "reason" are intuitive and sensible categories. In fact, it's a very common theme in any subject material that resembles philosophy. One of my favorite quotation comes from Kahlil Gibran on the subject:
Your reason and your passion are the rudder and the sails of your seafaring soul. If either your sails or your rudder be broken, you can but toss and drift, or else be held at a standstill in mid-seas. For reason, ruling alone, is a force confining and passion, unattended, is a flame that burns to its own destruction. Therefore let your soul exalt your reason to the height of passion, that it may sing; And let it direct your passion with reason, that your passion may live through its own daily resurrection and like the phoenix rise above its own ashes.
Do the Categories of Emotions and Reason Have an Empirical Basis?
In modern science, absolutely, and the empirical basis can be understood through neural correlates of conscious experience. Without getting too much into neural anatomy and physiology, it should be understood that there are definite regions of the brain that can be ascribed to, though contestable language in philosophy, "producing" emotions. The amygdala for instance is highly correlated to the experience of fear. From WP:
The amygdala has a primary role in the processing of memory, decision-making, and emotional responses (including fear, anxiety, and aggression). The amygdala was first identified and named by Karl Friedrich Burdach in 1822.5
That means, in real time, using fMRIs and other tools, we can see the brain change in empirically consistent ways with the experience of key emotions. That's the equivalent of watching data flow through a microprocessor when a computer system is controlling equipment. If you really want to get empirical in your exploration, consider reviewing Damasio's somatic marker hypothesis. There is a preliminary scientific basis for claiming not only are emotions and logic different, but that it is the emotions that determine the decision executed in logical thinking.