I'm talking about using them at the start of the sentence, meaning "so" or "therefore".
「今日は暇だ」 「だから、映画でも見に行こう?」/「なので、映画でも見に行こう?」
I'm assuming that the difference is simply the same as the difference when they are used as a conjunction in the middle. That is to say, なので is slightly more objective and polite.