In three weeks' time, "coming home" is the activity you will be doing. "will be coming home" emphasises the fact that an activity or situation takes place over a period of time. Here is another one: "This time next week, I will be lying on the beach, sipping a cool beer, thinking of all you people working hard in offices." "will come home" simply describes the future fact or plan. If you're not sure, use will + verb.

As Michael has shown, it is possible to find a difference in meaning between the two forms. In other contexts these differences might be significant or useful, but here the two sentences are interchangeable. One has more words, the other has fewer: some people like to talk, some people like to talk less, that's the main difference.