I would say that they're both as polite as each other. For your example, it would be more polite to say "I'm tired"; I think that's a pretty good rule. "I need/want to sleep" isn't impolite, though, it's just less formal. You might not say it to a police officer, but you'd probably say it to your boss.

Hi Vanessa, I would say "need to sleep" is a little more polite. "I want" can seem a little self centered, whereas "I need" would be less so. you could preface with "I'm sorry" which will soften it a bit, then "but I really need to sleep".

What could one say in English, at bedtime that is explicitly rude in language? "Shut up and go away. I am going to bed now." "I'm tired of your continual talking to me. I am going to bed." "You are keeping me awake and that annoys me. I want to go to sleep." "Why don't you leave me along and let me sleep. I need to go to sleep." These are impolite expressions that express impoliteness. Neither of your phrasings, as Niall shows you, need be regarded as impolite unless the tone is offensive or hostile. .

Vanessa: Niall is correct. Any impoliteness can be derived from the tone of voice. Either expression can be offered politely. A native speaker can also, by tone of voice, offer either expression in such a way that it would be regarded as rude. A native speaker would know how to say this softly, in a Matter---of--Fact manner, but would also know how to say it harshly, so as to make you feel that they were Biting---Your---Head---Off. .

neither you just say "It's late, and it's time for bed." = "I should go to bed now".