To clarify my statement: Where I'm coming from is that pretty much any war or "police action"/whatever the United States Military has gotten involved in since World War II has been essentially pointless. It wasn't to fight over a "greater good" to stamp out an evil force putting its will on the world and with such grand goals in mind it was over squabbles or resources.
Argument could be made that Vietnam and Korea perhaps weren't that extreme, but even in both of those cases the scale of the "threat" wasn't nearly as grand as the threat posed by world powers in either of the World Wars or over America fighting for its freedom or unity in Revolutionary War, War of 1812 or Civil War.
People currently like to say things like "support our troops, they fight for our freedom!" I support our troops but I don't see how any action the U.S. Military has taken in my lifetime in foreign nations has had any impact on my
freedom. If we didn't get involved in either war with Iraq or the war against Afghanistan I'm pretty sure America would still be here in very much the same form.
I'm guessing Picard is looking at it in a similar fashion. In "The Manhunt" Picard does speak rather admirably about the United States military involvement in World War II, he likely saw that war as being a "necessary evil." It was America stepping in to not only counter the attack on Pearl Harbor but to stop Hitler's advancements on Europe and Asia (which is TOS is to be believed would have led to Hitler taking the world if America didn't step in.)
So you look at that, then you look over the first Gulf War pretty much over -as Q put it- "squabbling over how to divide the resources of your little world" which is not an uncommon interpretation for EITHER war in the Middle East, it's not hard to see how Picard would look down on that. Because what WAS the point of either war in the Middle East? On what basis DID we invade Iraq to take down Saddam Hussein as he made no credible threat against the U.S., nor realistically presented any. Sure, in some ways we see it as a way to "free" the Iraqi people from Saddam and the tyranny he presented but given what we know about the Federation and human culture of the 24c that likely wouldn't look too kindly on a government using its military might to depose a sovereign nation's leader simply because we disagree with his politics and leadership.
Hell, we know the Federation from the Klingon Civil War actively AVOIDED getting involved in politics, this when they KNOW the Duras House had a treasonous relationship with the Romulans!
So, yeah, that's why I think Picard looked down on the 20th Century military uniform. He doesn't see it as a man fighting to defend lives and freedom and to prevent murderous dictators from taking over the world, he sees it as man whose country goes into a nation and takes down a leader simply because we don't really agree with him.