Just ran into this advantage as well:
Information obtained from the ATF National Firearms Handbook
Section 13.8. Requesting permission to transport certain firearms in interstate or foreign commerce.
A person, other than an FFL/SOT, may not lawfully transport in interstate or foreign commerce any destructive device, machinegun, short-barreled shotgun, or short-barreled rifle, without prior written approval of ATF, specifically the NFA Branch.214 For definitions of these firearms and devices, refer to 27 CFR 478.11. Licensed collectors are not required to obtain such approval if the firearms and devices being transported are “curio or relic” firearms under the GCA.
So it appears that there are also fewer transport limitations if it (and you) are C&R.