Only downside to an LLC...
Is the requireemnt to file tax returns (as it is a business entity) - Federal & State.
If for some reason the LLC falls out of good standing (paperwork is out of date, fail to file on time, etc.) all property of the LLC (esp. the NFA items) will be deemed contraband and are subject to legal confiscation.
A simpler, equally legal and cheaper is setting up a Revocable Trust...takes 10 minutes can be done for <$50 and get around the CLEO sign-off and fingerprint rules that apply to an individual.
NOTE: I am not an expert but have done a ton of research and just completed my trust...first NFA purchase will be in the works this week: Form 1 to build an SBR.