The phrase "What good will this do anybody?" implies something that is close to you. In other words, you might be holding something in your hand and asking someone a question.
The phrase "What good is that going to do anyone?" implies something that is far away from you. In other words, you might be pointing to something that is not next to you or the person you are talking to and asking them a question. Also, this question implies that it can also be an action.
As such, the meanings are very similar and in some cases might be able to be used interchangeably, but that might not always be the case.