Dear RRStubbs: I guess it depends on what type of position you're applying for and what the company is looking for. For example, if you know they include those words "Veterans are encouraged to apply" or other indicators that the company is Vet-Friendly, it may not matter. But, you might also check on LInkedIn or other websites to see who currently works there. If you see a lot of Veterans with their military credentials listed on their LinkedIn profile, it might be good to include specifics about your military experience and rank.
Years ago, there was a big push for Junior Military Officers (JMOs) - something you might see in an advertisement in the __________Times military paper. As a former JMO, I made sure to include that. Let me be quick to add that you might also see ads with "Senior NCO" or "Technical" military experienced personnel, or simply "Veterans" are encouraged to apply.
But, be ready to explain your rank (Most civilian employers probably don't know the difference between an Army Captain versus a Navy Captain), but more importantly, what you did. Your job performance, your job description, and especially explaining all this in plain English is critical.
One last thought, I once was asked by a Senior NCO, "Hey Sir, what's the difference between a Second Lieutenant and a Private Second Class?" (I knew the answer but figured I'd play along and said What?) "The Private Second Class has been promoted once!"
The point I'm trying to make here is that you should focus less on rank and more on what you bring to the prospective company. You may in fact need to overcome some perceptions as to who does what in the military. By doing a little fact-finding, you might uncover that they have a perception of what a person of certain rank may do as opposed to the truth about your specific background and ability to fulfill the job requirements.
On the political campaign, I've seen several people reference their military rank, but not without including what they did.
"Civilianize" it as much as possible. Combine rank with some facts about you, what you did, and what you can do.
Hope this helps!