Sebastian says, "For all intents and purposes, 4473 is registration."
With all due respect to Sebastian I don't think he has thought this through because there are huge differences. Even in the confiscation scenario which is one of the main objections to registration.
Here are some of the differences:

• In most states a 4473 is not required for private transfers. Registration would be meaningless if the paper trail disappeared after the first retail sale like it does with 4473s.
• With registration you can be challenged for your papers and a gun inspection every time you buy ammo, buy an gun accessory, are at the range, and every time registration is renewed (Yearly? Monthly?). If you try to buy ammo for a 30-06 and you can't show papers that demonstrate you own a 30-06 then you aren't going to be practicing with that gun for the day when cattle cars start hauling the Jews/Christians/homosexuals/blacks/whites/whoever to the camps and you finally decide shooting the bastards is justified.
• Registration fees can be made exorbitant. Initially they would be small enough that few can legitimately complain about the price. But once the guns are on "the books" they can make the fee anything--even 100 X the price of the gun every year and still not have "banned guns" and violated the letter of the Heller decision. The power to tax and/or license is the power to destroy.
• Even if guns aren't banned they can mandate "safe storage" with alarms, event bank vault like gun safes and 24 x 7 guards. They can't demand to inspect your gun safe if they don't know you have a gun.
• It may not be obvious, but registration violates my Jews in the Attic Test while the 4473s do not.

As it currently stands should the government demand all 4473s be turned in there will be a lot of guns sold over 20 years ago that will be completely untraceable. And, I suspect, there will be many cases where large numbers of 4473s disappeared in a surprising number of "unfortunate fires". And even if they come knocking on your door because your name was on a 4473 from a couple years ago you can lie or have them ask your lawyer where the gun is without much fear they can actually lay there hands on the hardware.

I say if in the previous paragraph because one cop told me they can't get a warrant for drugs that someone saw even 10 days ago. There must be credible belief the item(s) to be searched for are still present when the search is to be executed. Is it credible to believe a gun that you purchased two months ago still present? Maybe. Two years ago? In the absence of registration that is a big stretch.

If that isn't clear enough compare the results of registrations required by NFA34 to the results of 4473s.