ATX stands for Advanced Technology Extended, while BTX stands for Balanced Technology Extended. These products are very popular form factors designed by Intel for motherboards and desktop cases. The ATX was manufactured to replace the previous AT design, and the BTX was made about ten years later to address the heat issues experienced in the use of most recent processors.
BTX is designed in such a way that it generates a greater amount of airflow, thus reducing the number of obstacles, and then cooling the processor. In order to achieve a better functionality of BTX, there are some components rearrangements that are done on the motherboard so as to enhance airflow.
ATX is cheaper, while BTX is found costlier than its counterpart. Due to this factor and some others, ATX is still found to be used more in computers, while cases and motherboards that are compatible with BTX are rare.