It's a fair question, and I don't think there's an easy answer. You must probably check for usage amongst friends and colleagues, on Google, and in a collocations dictionary. This is true for all 'attributive nouns': why a 'football manager' but rarely a 'badminton manager'? (probably because there aren't that many).
I remember the example in the Family d'Alembert series: The Primary Computer Complex relayed instructions to the myriads of idiot versions of itself in preparation for the final battle against humanity (not an accurate quote, but you get the picture). 'Idiotic' just wouldn't work here. I think 'idiot' focuses more on the agent or sub-agent (drone computers) being referenced, 'idiotic' on the behaviour. So, idiot teenager but idiotic smile / plan / decision / comment.