I'll leave the respective chauvinists to their breast-beating and mutual barrage. I lived in Seattle briefly during my previous life in the US, have a few social and familial connections there and also made the occasional 3-4-day trips there since moving to Vancouver, so my reply is woefully misinformed. However, this is my take:
Weather: Slightly better than Vancouver--the Olympic Peninsula shuttles some of the rain storms North to BC (especially in Summer), the slight diminishment in latitude allows for a marginally warmer average temperature, and the area is more prone to ice storms and sleet than snow in the Winter as a result (mind you, we're still only talking a few weeks out of the year).
Societal Harmony: Erm, that's up to interpretation and your intimacy with the culture. I tend to see Americans as more straightforward about their differences in person, more willing to be "upfront" and get something that's bothering them off their chests and sorted out as compared to Canadians (though BCers can be more forthcoming than people from some other parts of Canada). I think most Americans would consider that Canadians "gloss over" social "differences" (I assume you're primarily referring to racial, gender-based, or political tension), and either pretend that they don't exist while people's anger festers away and expresses itself in, shall I say, "slippery" (nay, even passive-aggressive) ways. One side note: the ethnic makeup of Seattle has historically featured large Japanese and Scandinavian populations, along with a lot of Welsh and Eastern Europeans in the coal mining country east of the city--there's definitely a different "feel" to the mix as compared to Vancouver (more sushi and lutefisk).
I can certainly say from my experience that, once you factor out some of the more reactionary suburban areas, people in Seattle don't display the kind of open, aggressive homophobia that I've seen in Vancouver. I can say the same about attitudes towards women (which is why I'm carrying on a long-distance relationship with an American rather than subject myself to Canadian guys). Also, because urban American youth are forced to become more "street smart" at earlier ages than Canadians, there's a marked difference in a certain genre of "social sophistication"--Canadians would call it cynicism, Americans might call it emotional maturity. As you can see, it's highly subjective . . .
Health Services--Don't insult my intelligence here. Horror stories abound. I worked in health care for a while in the US, and I saw it up close in my family environment. I've also been on the wrong end of the social Darwinism equation where health services are concerned. One thing I can tell you: all the East Asian, subcontinental, African and Eastern European medical professionals who weren't interested in driving cabs in Canada are successfully practising in the US.
Sporting Accomplishment--As a very young child, I attended a Major League Soccer (or whatever they called it then) match in the Seattle Kingdome some 25 or 30 years ago. Evidently Seattle had one of the largest community leagues in the country at that time. Nothing like what you're used to, of course. Their NFL team was in the Superbowl last year, they have a pretty muscular college football programme (which, to my mind, is way more interesting than pro football); there's an NBA team; a baseball franchise (American League, unfortunately) and only minor league hockey. Hockey fans in Seattle pick up Vancouver Canucks games on cable or make the trip up here when they want to see NHL games.
There's good skiing, sailing, mountain-biking and all manner of outdoor pursuits in both cities. The only difference is that in the US you're allowed to carry a gun for protection against bears, pumas and meth-addled hillbillies when you venture into the wilderness. In Canada you trust your personal safety to a spray bottle of mace.
General Standard of Dress--Canadians do their clothes shopping down in Seattle, and don't believe anyone who claims otherwise. I don't think either city is more "formal", but Canadians are significantly more conservative in their dress. You'll especially see more distinctiveness of dress, comportment and general "style" amongst the different subcultures in Seattle--here in Vancouver the differences are more muted.
Average Height--I know where you're going with that one. I'm not going to take the bait of those old misogynistic threads from DV.
Level of Chestnut Devotion--??? Waaay more variety amongst the squirrel population here in Vancouver. They're all grey with big fluffy tails in Seattle, but here in Vancouver there are these stylish-looking black ones too.
I'll add two more:
Customary colour of the sky during the day--Uniformly grey in both places.
Topography--Vancouver: river valley-ish. Seattle: positively San Franciscan.
On old-fashioned mnemonic for remembering the order of streets in downtown Seattle: "Jesus Christ Made Seattle Under Protest"
General rule of thumb for street names in Vancouver: Welcome to the colonies, mate.