"Will do" and "going to do"

I think they both describe the same situation, but there is a difference in register - the first sentence is more formal.

In the second sentence it sounds to me like the girls have decided to do their homework after lunch; in the first sentence it sounds like they've been told to, or they always do it then.

You might find this document useful to explain some of the differences in usage between the two future tenses in English which seem to be roughly the same in French:

https://www.laits.utexas.edu/tex/pdf/taf4.pdf

Hi Arndís,

I agree with Alan in that there is slight difference in register between, e.g.:

Je vais te dire. -- I am going to tell you.
Je te dirai. -- I'll tell you.

In addition, it seems that there is also slight different in temporal proximity. La future proche (Je vais te dire) is slightly closer to the present than la future simple (Je te dirai).

-- Chris