Prevention of gun violence isn’t exactly the remit of either of those agencies. The ATF focuses on the tracking of and illegal sales of guns while the FBI focuses on crimes committed with them (and other crimes, of course). Neither of those are about prevention of gun violence.
A separate agency that can focus more on the social issues that are behind gun violence could act in many ways that neither of the other two agencies could while not having to worry about drawing focus or manpower, from how those two agencies operate.