Which is awfuller? Believing true is false or false is true? Why?

It's all about context.

probably the 2nd one

Context dependent.  In a law court a guilty person might go free, or an innocent person convicted.  In one's personal life one may hold biases views against or favorable views mistakenly.  And I suspect we all have read of disastrous consequences of believing false medical claims or false religious leaders and doctrines.  And the same of political leaders and social doctrines. 

Saying either is awful  is sort of like blaming the victim.