Thanks for your detailed explanation.

While they can mean similar things in certain contexts, they aren't quite used interchangeably. I'd say that the word "deteriorate" is more common, and is a verb that can be used to refer to worsening condition of something. While the word "degenerate" can technically be used as a verb as well, it's much more commonly used as an adjective or noun referring to something that is morally corrupt. In my own personal experience I have rarely heard it used as a verb.

Degenerate is applied to a persons character or moral substance. A person can degenerate into a different person, for many reasons, bad influences wrong choice of friends or drug abuse etc. Deteriorate can be applied to a person in regards to a worsening mental condition illness or disease etc. It can also be applied to things like food going bad or relationships between people and countries getting worse. You can refer to a person as a degenerate meaning they are a bad person etc. But you cannot refer a person as a deteriorate. So degenerate does not mean to get worse in daily usage.