This is a difficult question to answer. The words "degree" and "level" have very similar (nearly identical) meanings. They are (more or less) interchangeable. In my opinion, "level" is a more rigidly defined word (levels are more strictly defined) whereas "degree" acknowledges the small differences between levels and more variable term. You can have many varying degrees of something, as opposed to a set number of levels.
Sorry if this is confusing- just remember that the two words are synonyms. Hope this helps!