there's not that much difference. a lot of americans shorten "I'm going to" into "I'm gonna" by effectively dropping the last syllable.
in writing, i advise using "will". formal writing prefers will. also, will is shorter than to be going to, and shorter sentences are more clear. clarity is a virtue in writing.
there's a more interesting difference between will and shall. according to the Elements of Style by W. Strunk & E.B. White
"In formal writing, the future tense requires shall for the first person, will for the second and third. the formula to express the speaker's belief regarding a future action or state is I shall; I will expresses determination or consent. A swimming in distress cries, "I shall drown; no one will save me!" A suicide puts it the other way: "I will drown; no one shall save me!" In relaxed speech, however, the words shall and will are seldom used precisely; our ear guides us or fails to guide us, as the case may be, and we are quite likely to drown when we want to survive and survive when we want to drown."