>>1
If A = liar and B = truthful, then
A says B always lies
B says A always lies
If A = truthful and B = liar, then
A says B always lies
B says A always lies
So unless you meant
"A says B always lies
B says A always tells the truth
one always lies, the other always tells the truth"
Then they are just people who are capable of telling the truth or lying at their own discretion like everyone does and neither of them is right. Whether they are lying or not depends on what they are thinking which is unknown.
They could of course be using hyperbole and A is criticising B, knows that B doesn't lie all the time, but means what he says since he assumes everyone else realises he is using hyperbole.
If you did mean
"A says B always lies
B says A always tells the truth
one always lies, the other always tells the truth"
Then A or B must be unaware of each other's foible in which case more information is required to make an accurate assessment, including the conditions of many of the factors already discussed.