What do you like best?
Mavericks stability and support is easily its best feature at the moment. More complex software that requires time to ensure compatibility with an OS has all at least been updated to be compatible with Mavericks, if not even Yosemite. As such, if you're worried about upgrading your OS and what it may do to your software compatibility, Mavericks shouldn't be a problem at all.
What do you dislike?
Mavericks does lack the features that make El Capitan or even Yosemite great. Spotlight isn't as fast, Safari is not nearly as sharp or quick, and the OS generally does not run as fast, even on older machines. That being said, the OS is incredibly stable, and does not cause any problems, which is why we still run it on one of our less-frequently used machines.
Recommendations to others considering the product
If you're worried about compatibility of complex software, use OS X Mavericks. If you only use standard and current software, go ahead and upgrade to OS X Yosemite or El Capitan, you will be pleased with their additional features and GUI.
What business problems are you solving with the product? What benefits have you realized?
Mavericks is incredibly stable, which helps us if we get into a pinch in an unusual situation. Very rarely, we have a problem with heavy workloads on our more current machines, and when we try to run the same process on our older machine running Mavericks it almost always works.