"You are a worker, I am a boss."
Translation:Sen işçisin, ben patronum.
Absolutely. If you have two parts of a sentence that are contrasting, you need to state both subjects.
"Müdür" is a specific job title. It can be used for "director" of a company, "principal" of a school, a police "chief", etc.
"Patron" isn't a job title, but is a more general term that can be applied to a "boss" or "employer" in any setting, including "müdür" bosses. :-)