Maximilian H. answered 09/11/19
High School English Teacher
These two are more or less interchangeable in their actual denotation (what the word or phrase literally means). However, there are some slight differences in connotation (the layered meaning suggested by the word or phrase).
"Break the cycle" usually refers to a negative cycle that's being broken, whereas "end the cycle" doesn't always carry that same nuance. In this case, though, if you're using both in context, I think you should be fine.
You can also find other ways to say what you're meaning ... if you feel like your writing is sounding repetitive, it usually is!