It's also become very clear from their response to Snowden's revelations that NSA is not going to get any closer oversight any time soon. The FBI and its partners cannot hope to maintain a comparable cloak of invulnerability. To Bruce's suggestion, I vote yea.
http://en.wikipedia.org/wiki/J._Edgar_Hoover
Giving NSA powers (or archives) to the NSA is a really, really, really bad idea.
The court system and legal system in the US these days is a joke and a farce--just look at the number of cases that make it to trial. We can't afford to give this sort of power over to any law enforcement agency.
What's more, FBI is also a MUCH leakier boat when it comes to intel gathering, storage, analysis, and sharing. Law enforcement personnel and practice could not possibly hide the decade+ worth of mass surveillance practices from US senators, congress, and the office of the President as NSA has.
As it happens I know something about the mindset within both orgs. With FBI, eventually the truth will come out. Not so with NSA - unless another Snowden is willing to commit suicide, professionally and personally.