For me, the expressions are used in different situations. a) "A big party was planned for 24 June but in the end, all the people that wanted to come were too old for parties, and so nothing came of it (the plan)." [the plan was not finalised and nothing happened] b) Though the decision was a democratic one, most commentators suggest that nothing good will come out of it." [there is something real here but it will not produce anything (in this case, anything good).]

Here in America, "nothing will come out of it" is actually the more common choice. When I do a Google search with American location data: "nothing will come of it"=320,000 google hits "nothing will come out of it"=626,000 GH I feel like "nothing will come of it" is more common in the UK. In the US, it feels a bit formal.