Dice, que debéis ir.
= He says you shall (should) go.
Dice, que tenéis que ir.
= He says you have to go.

The second one is rather harsh. Either the person really has something to do very urgently or the host is trying to get rid of him in a very direct manner.

Si alguien se desmaya en la calle, se tiene que ayudarle.
= If somebody faints on the street, the person has to be helped.
Si alguien se desmayó en la calle, se debe ayudarle.
= If somebody faints on the street, the person should be helped.

Well, probably a question of moral and ethics and which street and which town we are talking about. But in general I would say - right, he should be helped.

Habría debido decirme que no iba a venir.
= He should have told me that he doesn't come.
Habría tenido que decirme que no iba a venir.
= He had to have told me that he doesn't come.

Here we meet morphology that is so terrible in the second sentence that there is no question which of the two sentences would be used.

Me debe dejar en paz, entonces yo le dejo en paz también.
= He should leave me in peace then I let him in peace as well.
Tiene que dejarme en paz, entonces yo le dejo en paz también.
= He has to leave me in peace then I let him in peace as well.

Ok, now here it comes the other one has a choice whether or not he leaves me in peace. Therefore, he should do so but in the end it's up to him.

Por mí no tienes que hacerlo si no quieres.
= For me you do not have to do it if you do not want it.
Por mí no debes hacerlo si no quieres.
= For me you shouldn't do it if you don't want it.

As we can see the meaning does change rather than the degree of freedom of choice or the level of politeness.