Hello,
There's no different polite degree between the 2 expressions.
가는데 is able to be used itself as declarative sentence, and a question tag, while 간다 is only used in declarative sentences.
For example, 나 학교 간다. = I go to school.
나 학교 가는데 = I go to school This sentence could be finished or not.
나 학교 가는데?= I go to school? as a question tag functioning the answer.
When using the questioning expression at times it works grammatically just like in French or other languages.
Ex) Je vais à l'école?