On this subject, as I was getting out of the Corps, a Vet told me: "All service is commendable, but not equal"
Going to Grad school showed me that while that is true, the division lines are non-existent if not relatively faint. The division between the Intra-branch Officer Corps and the E-Dogs (a phrase I was enlightened to from a former Marine Officer) is a little deeper than the branch rivalry itself. What I found to be strange is, as Veterans, officers from one branch have little-to-no division with enlisted from a different branches, but the O-E divide within a branch have a bigger divide. Saying I was a grunt Marine Corporal to a former Army O-3 is met with "That's fucking awesome" where as saying the same thing to a former Marine O-3 is often met with "oh". That's not even a common thing though, because typically anyone who served is happy to find others that served. We are all just fundamentally different than the population at large, thus the lines of division are faint.
We are all friends and we rag on each other mercilessly. The Army guys are made fun of for being self-important and prioritized, the Navy guys are made fun of for being nerds and homo-erotic, the Air Force guys are made fun of for being pampered and pussified, and the Marines are made fun of for having extra chromosomes, finding new ways to be gay, and jerking each other off about how much better we are than everyone else when we find another Marine. The Coasties are probably subject to some form of jokes, but no one has seen any, ever, so they're more myth than fact.
I still get a kick out of telling my 0-4 Navy counterpart in the program what it was like for my day-to-day life. He acts as if I just got back from the trenches of World War 1. I tell him it sounds like he enjoyed life in as a Aristocratic Noble. Yet we still share the tab for beers.
Last thing I'll say: Marines are definitely the most offensive of the lot. I got some pretty dour looks when I said the local strip club lets you lick the Tuesday Night special's C-Section scars for a buck an inch. The only guys that laughed were the Marines and the Army dudes, but the Army dudes said "that's fucked up". The Marines counted their singles.