Zeus is considered all powerful in Greek mythology. Apollo is the son of Zeus and this means that he should be fairly powerful. He is the god of sun, prophecy, music and healing. While these things are quite powerful forces, he still needs to obey the words of his father, Zeus. Moreso, the strength and power of Apollo comes from his father.
A particular incident is mentioned where Apollo had managed to kill a Cyclopes in anger. Zeus, when he came to know of this incident, punished Apollo by taking away his powers and forcing him to serve as a mere mortal for a year. This particular incident clarifies that while Apollo, quite powerful in his own right, is still subservient to Zeus for this powers.
Conclusion
It is thus concluded that Zeus is stronger than Apollo and if there ever is a fight between these gods, then Zeus will be the clear winner. For more stories related to Zeus, like how Zeus became King of Gods, you can read my blog.