I can say with confidence that the shorter trip will take less fuel to get there for both a ecodriver and normal driver.
19 miles @ 28 mpg (the highway epa rating for the 2.4l engine) means .68 gallons used.
11.5 miles @ 21 mpg (the city epa rating for the 2.4l engine) means .54 galons used.
Now, if you are an ecodriver and use some of our techniques, you can EASILY beat 29 mpg in city driving. So, all roads lead to short and slow.
BTW, welcome to the site. The Matrix is a great car, I just replaced mine this summer.