What is the difference between
comenzar? Is one more formal than the other?
Empezar, as Eric explained is related to events. Like the beginning of history or the beginning of a work project.
Comenzar is more personalized towards a subject.
Though they mean the same, we Spanish speakers tend to use each in those contexts.
Absolutely interchangeable as Eric states in his answer. I agree. However, I'd add that empezar is a little more common than comenzar. Actually Ngrams says in written Spanish, in the last 60 years, the frequency of use has been reversed. That is:
And comenzar is slightly more formal. But I have no other sources than native speaker's gut.
An existing answer, sadly the accepted one, has stated that empezar is more widely used than comenzar for things like "a project". That just doesn't make sense
My conclusion is not that some is used more than the other. The difference is not significant enough as for being considered as a definitive answer. That's my point.