The Navy is one Department that appears to be very, very careful about creating absolutely equal opportunity out of USNA or NROTC for desired billets.
The latest published data I have show the % of 2LT out of USNA and NROTC to be within 1 percentage point of each other into Aviation, EOD, NUC, SWO, Educational Deferral (that includes Med School, Law School, Dental, Veterinary), etc. Within 1 %... i.e. 30% were assigned Pilot out of Annapolis, 29% assigned Pilot out of NROTC. There is a slight advantage for SEALS out of USNA, but only 10-12 billets to NROTC equalizes them.
This tells me there is zero advantage, within your peer group, of going to USNA vs. NROTC as far as billeting.
These are the results for FY 2011
Service Community/USNA# Billeted/USNA % Billeted/NROTC # Billeted/NROTC % Billeted
Pilot / 227 / 30% / 273 / 29%
Naval Flight Officer / 75 / 10% / 108 / 12%
Surface (Conventional) / 225 / 29% / 280 / 30%
Surface (Nuclear) / 32 / 4% / 34 / 4%
Submarines (8 women) / 132 / 17% / 143 / 15%
SEAL / 30 / 4% / 22 / 2%
EOD / 14 / 2% / 18 / 2%
Restricted Line / 22 / 3% / 32 / 3%
Medical Student / 10 / 1.3% / 18 / 1.9%