As much as I dislike the current President, I can say that I see why the responses were different with his entrance. In the George Bush entrance, they weren't playing "Hail to the Chief". As simple as that sounds, Marines know customs and courtesies. Play "Hail to the Chief" - they stand at attention, period. However, I think what's more telling (on both sides) is the departure. Bush seems to be popular, and wants to pose with the troops. Obama doesn't seem as popular, and only wants to greet the CJCS. Throw in two different environments (Camp Lejeune vs. Al Asad) and you can't draw much from it.
I have my personal opinion though - Obama is like Gore with regards to the military. Why do I say that? At a hail and farewell when I was a young Lt, I spied a picture of the host with President Clinton, when he was flying at HMX-1. We asked him what he thought and his exact words were: "President Clinton was a total choad until he realized that those around him in uniform had no hidden agenda. We were there to do our jobs, and he respected that. He turned out to be a pretty decent dude. Al Gore, on the other hand? Total ass-nugget." Yes, this was after the imbibing part of the hail and farewell, and after Bush was already President.