ATF requires the yellow forms to be kept for 20 years at which time they can be destroyed. The A&D book shows the name of the person or company that the gun came from and the name of who it went to. It also shows the serial number, caliber, type of gun, and maker. The dates that it came in (acquired) and went out (dispositioned) are also in the book. The A&D book does go to ATF when the FFL goes out of business. The Form 4473's under 20 years old also go to the ATF when an FFL goes out of business. The A&D book and 4473's are used to help trace firearms that turn up in crimes or ones reported stolen.
NICS background checks only tell the FBI the name of the person buying the gun plus the DOB, height, weight, social, state of residence, and place of birth. The only info given on the gun at this point is the type of firearm: long gun, handgun, or both.
If ATF wants info on a gun transaction they have to go out and personally inspect a dealer's A&D book and Form 4473's. The stolen gun and crime scene gun traces, however are done over the phone.