They can both mean troubled or worried, based on my reading of Google Translate. But are there subtle differences in usage or context between them?
You seem to have some sort of confusion here.
"Molestar" literally means:
"Molestado" needs some elaboration particularly in its use. It is gramatically incorrect to say "estoy molestado"; you say "estoy molesto" ("I'm annoyed" or "I'm pissed") or "estoy preocupado" ("I'm worried", "I'm troubled").
In the context of having someone make you upset, you would rather say "me han molestado" or "he sido molestado" which both mean more or less "somebody has hassled me" or "I have been disturbed" or even "somebody made me upset" or "I have been bothered".
Maybe if you could give a little more context into why you think both terms mean troubled or worried you could get a better answer.
Hope this helps.