The differences in the essays can be summarized by the differences in the use of personal pronouns:

I/me/my:  McCain 3  Obama: 25

McCain makes appeals to abstract notions and higher concepts, and subordinates the individual to the greater.  Obama places at the top the society of individuals and grounds abstract notions to their immediate and real world analogs.


McCain goes for the abstract

Patriotism is ... putting the country first, before party or personal ambition, before anything. It is the willing acceptance of Americans...to try to make a nation in which all people share in the promise and responsibilities of freedom.

Obama's goes for the personal and the interpersonal, and grounds abstractions in an individual reality:

...patriotism in my mind--not just a love of America in the abstract, but a very particular love for, and faith in, one another as Americans.

...we have the unparalleled freedom to pursue our dreams.

......That is the liberty we defend--the liberty of each of us to follow our dreams.

McCain places the individual at the service of the higher, intangible:

To love one's country is to love one's countrymen.

Obama emphasizes the country is the sum total of the people who made it, and its purpose is to serve those people; abstractions are grounded in reality:

The greatness of our country--its victories in war, its enormous wealth, its scientific and cultural achievements--have resulted from the toil, drive, struggle, restlessness, humor, and quiet heroism of the American people.  

McCain makes the reference point a higher, intangible purpose or good, while Obama repeatedly reinforces that the country is the people:

McCain: ...blessed that so many (soldiers) have so often believed in a cause far greater than self-interest, far greater than ourselves. 

Obama: ...a willingness to sacrifice for our common good.

McCain asks what will come:

 

...if we are to be genuine patriots, we must remember also that we are patriots because we love the countrymen we will never know, who will be born after we are gone.

Obama asks what got us here and what it means now:

We can tuck in our children at night and know that they are fed and clothed and safe from harm. We can say and write what we think, without hearing a sudden knock on the door. We can have an idea and start our own businesses without paying a bribe. In America, anything is possible.

I know that stories like mine can happen only in the United States of America. 

And, of course, McCain makes explicit that government is supposed to be limited:

where... a love of liberty and self-reliance still check the excesses of both government and man.

...In return, the gift we can give back to our country is a patriotism that requires us to be good citizens in public office or in the community spaces where government is absent.

While Obama makes no distinction between the government or its people:

Those who have signed up to fight for our country in distant lands inspire me, just as I am inspired by those fighting for a better America here at home by teaching in underserved schools, caring for the sick in understaffed hospitals, or promoting more sustainable energy policies in their communities.

...That is the community we strive to build...

It is often said that this election (or recent elections in general) are not really about ideas, but it seems that this election is nothing else but an ideas battle.  In many ways they want the same thing, but they differ in the presentation: "energy independence" vs. "sustainable energy policy"; "make sacrifices" vs. "pay their fair share;" etc.  That's important because the "why" of a policy, even when the policy is the same, defines our "common good" and influences future policies.