From my point of view, I'm just perplexed. Leaving aside issues of xenophobia, I'm very perplexed by the economic view of the "Leave" camp. Everything I've seen indicates that 90% of economists, both inside and outside of Britain, have said that the best case scenario for Britain leaving the E.U. is that it will be BAD for Britain's economy. When the best case scenario is bad...one wonders if maybe you should look a different way.

On the other had we all know how persuasive a vast majority of climate scientists have been.

The simple fact is that the Leave voters either didn't believe them or actively voted against "elitists" and the establishment. If you saw the barrage of disinformation and shameless lies that were spouted by the leave campaign and their supporters in the vested interests of the right wing populist press over here, you would understand why they might feel that way - the similarity to the climate change deniers and their oil-company backing is entirely comparable.

The Remain campaign wasn't much better on their content, they were just wildly incompetent at getting their message across.

I feel I must defend NATO a little, here.

I agree that the EU as an ideal is meant to bring former enemies together and bind them in one family, making war between them highly unlikely. Its achievements in furthering peace are due to the integration of once-feuding societies, which is a good thing. NATO, meanwhile, also furthered peace in the world... by making an attack against one of its members a suicidal move. Different  strategies, similar results.

(However much I'd like to think that the relative peace we've observed since WWII is due to mankind finally growing up, I remain convinced that the single most important thing that kept us quiet is, paradoxically enough, nukes. When war is not an option, there can be no war, even if countries keep rattling their sabres).

Comparing NATO's record to the EU's would probably fill many issues of Foreign Affairs. I agree that just by existing, NATO has at times caused tensions with the Soviet, and later Russian, blocks; at the same time, it has no imperialistic agenda and has been a strong moderating power in world politics.

NATO also earned some bragging rights : the crisis in Bosnia-Herzegovina, and later Kosovo,  were not resolved by Strasbourg nor Brussels (nor by the mostly-ineffectual UN, which were at the time paralyzed by China's and Russia's veto on the matter).

Not that NATO or the EU need be better than the other at peace mongering; any organization that helps prevent new wars is to be lauded, certainly. 

Well, I can speak for France and Sweden in some regard.
Sweden genuinely hates NATO and hates that it was forced to be part of it. It's been well documented over here over the years how the CIA used it to trigger assasinations and build disruptive underground cells. Also, as Sweden is a social democrat (socialist!) country, it's been often subjected to very sneaky communication campaigns, as the CIA couldn't have one of the most peacefull and pleasent place in the world during the 50-80ies be a socialist one. Since Sweden joined NATO earlier this year, I know a few people who have actually moved away from Sweden as a political gesture. It may be extreme, but it exists.
For France it's a much different affair, as the country was at its inception. But as much as it felt it was needed, France had US military bases for many many years, as did many countries in Europe. The problem is that the US stated they wanted Europe to handle their defense on their own, but still kept those bases, some with missiles targeted at Moscow (Turkey), which was very disruptive. So with France being run by the General De Gaulle, first elected president of the fifth republic, by 1966, we kind of left because as a great power, he felt we couldn't risk the constant spying and such. With the Eastern block that close, we needed to be really independant, and the EU was a great way to prove it.
So yes, there is a general feel of mistrust with NATO in those countries. It's not very  loud, but still underlying on a global scale.
The way the yougoslavian civil war was handled by the US, the UN and France tells a lot abou the diverging philosophies about this.

I've never heard it so glowingly described by anyone here in the states and in my travels in Europe the gossip and news I'd hear weren't that positive about the European Union either but that's just my experience as AGS' opinion shows there are obviously those who have a very positive view of the EU and I don't see any polls that would say which view is the more commonly held.

Well not necessarly : Germany wants a strong euro while France wants a low one, depends if you intend to import more then export. The currency thing isn't really an issue, unless the fall is sudden and massive.