esday, i was in the same exact predicament (sp?) my first choice was navy because my former boss enchanted me with his experience as a naval aviator,,, then i was rejected by the navy, i know that all i have to do is score better on the astb (and god willing) i would get in,, but.......i talked to the oso (and other marines that are in active duty now) over on the marines side, and now i have completely changed my mind and would love the oportunity to be a marine officer...(and if you want to know why i changed my mind, private message me)
anyways the major conflict when you apply to two at the same time:
Astb Scores: You cannot take this test (if your taking it for the first time) twice without a 30 day wait period after taking it your first time, I wouldn't count on the navy or the marines giving your scores to the other branch, so theoretically you would have to wait a month after applying to one branch , to apply to the other..but what i would suggest is that you take the astb, then stall the application, or maybe you still need time for the recommendations to come in etc, this way the gap between applications is less than a month, the reason you would do this is because i believe they expect you to sign the dotted line within 30 days of being offered your slot...
Also you may have problems with transferring your physical over,, the navy would not give my physical over to the marines, so i will probably have to take it over again,, oh well
Finally the physical tests are two entirely different ballgames, the navy is (in my opinion very easy) compared to the marine physical test, navy : 1.5 mile run (max time 12 mins) 47 pushups (i think) and 48 (situps may be off here),, whereas the marines : 3miles (24 mins max time) 10 pullups (min) (80 situps ?? not sure what the min is)
Let your heart tell you which service you want to serve in,
Best of Luck