For examples, if A washed the dishes and came to B to tell him that, but B didn't believe it. Should B say " I don't believe that you washed the dishes" Or just "I don't believe you" Is there a difference between them? Do both sentences have the same degree of indelicacy?
You can say either.
The difference seems obvious:
The first statement disbelieves a certain thing about A (that you washed the dishes); the other disbelieves the person A himself in a certain context (don't believe you). Taken by themselves, with no other knowledge of the relationship between A and B, and no further statements made by either person about the issue, it seems disbelieving the person is stronger than disbelieving a statement or action that the person has claimed to have done. On the other hand, in the real world, with a history between A and B, either sentence could be lethal. There's simply too much meaning that is not included in the words of either sentence to say which one might be more indelicate.