Both sentences are correct and have the same meaning. The comma just adds a slight pause. The use of 'therefore' in both sentences makes them quite formal, I wouldn't say either sentence is politer than the other. In conversation most people would say something like "it's raining so I'm not going out". You can't always replace 'and' with a comma though. "It's raining" and "therefore I won't go out" are two independent clauses. They could be two sentences but you can connect them by using a conjugation (and, but, for, nor, yet, or, so). Obviously not all of these conjugations will be grammatically correct in the example sentence.

It's raining ; therefore, I won't go out. ( conjunctive adverb cannot join 2 independent sentences , so you use semicolon to slice them into 2 parts) It's raining. Therefore, I won't go out. ( 2 independent sentences) It's raining , and therefore I won't go out. ( use 'and' to join 2 sentences) Use a semicolon (;) before a conjunctive adverbs and a comma after .. however, therefore , thus ,furthermore etc Use a comma before coordinating conjunction .. and, but, or, nor, for, so, yet All have the same meaning > no less polite than the other . When speaking , they all sound the same, but when in written form , the punctuations pose the problems.