"美味しいじゃん?" and "美味しいでしょう?" No matter how I translate it in English it still means "it’s delicious, right?" So what’s the main difference between them both? (I do know that "でしょう" in dictionary means "probably". But I heard you can use it as "right?" In daily conversations)
美味しいでしょう is a natural and standard Japanese to say "it’s delicious, right?". (I'm not sure what you mean でしょう as probably so far.)
美味しいじゃん? is basically the same but it's a colloquial form. But I can imagine "it’s delicious, right?" in the meaning of "Please agree with me it's delicious?" or "I'm very surprised it's surprisingly delicious, right?" or probably some other depending on intonations.
If you want to try to avoid being very rude ending with じゃん, I think you just pronounce it just softly even in a casual situation.