1) First of all: DO YOU HAVE A VISA TO ENTER THE U.S.?
...If so, then you may leave the airport.
2) You will be flying INTO and OUT OF Terminal C.
...That is the International Terminal. Lines are not a problem there.
3) WHAT DAY OF THE WEEK WILL YOU BE IN TEXAS?
...Mondays suck, like in most cities around the world. Museums are usually closed and this can put a damper on things.
4) Renting a car: Kayak vs Priceline's "Name Your Price"
...DFW is an international airport (obviously) and rental cars tend to be fairly expensive, so book as far ahead in advance as you can and check what kind of deal you can get on Priceline with the "Name Your Price" option.
DALLAS vs FORT WORTH:
DALLAS PROS:
-The "Arts District" has exploaded in the last 5-10 years and has finally surpassed Fort Worth's.
-In addition to the Dallas Museum of Art (FREE) & Nasher Sculpture Garden, there is also...
...the Mort Meyerson Symphony Hall that you might be able to peek into...
...as well as the AT&T Performance Center
-The Perot Science Museum (open 7 days a week) is about 4 blocks from the Art Museums and the Dallas Aquarium is another 2 blocks from there.
-The Texas School Book Depository / Grassy Knoll / Dealey Plaza / JFK Memorial are just another 5 blocks from there and you can wander through the restaurants in the "West End" (former warehouse district) to get there.
-"Big Red" (The former Dallas County Courthouse) has some museum stuff in there and is right there as well.
-After this, you would end up at Union Station, where you would take the DART Rail/Train back to the airport.
-Littered in the downtown area are buildings from the 1910s-1930s,
...about 3 I.M. Pei buildings
...cool old Courthouses
...a Masonic Temple
...a Scottish Rite building
...a Cattle Trail in front of the Convention Center made of several Bronze Sculptures of Longhorn Cattle
...a very funky looking City Hall (I.M. Pei)
...and very hot sidewalks.
DALLAS CONS:
-About twice as far from DFW as Downtown Fort Worth
-Downtown is fairly spread out and you could easily walk 5 miles doing a loop of the downtown area. (Which I would suggest... and as a tour guide of Buenos Aires, I know a thing or tour about walking tours.)
-If it's a hot day, you'd need to take a shower at the Admirals Club (you're obviously flying AA) before heading to Germany and that's US$50 for a one day pass.
FORT WORTH PROS:
-Just about 25kms from DFW airport. (Much closer than Dallas.)
-Three Museums right next to each other:
...Kimball Art Museum (Fort Worth's FINE ARTS museum) is small enough to see it without getting worn out.
...Amon Carter Museum (Western Art & Photography) with works from Remington, Charlie Russell, and other tops artists in this field.
...Fort Worth Contemporary Museum which features an art collection of about 50% Contemporary Artists from Texas over the last 40 years and other artists from around the world.
-The Fort Worth Stockyards (a car or taxi would be needed to get here) which gives a glimpse as to why Fort Worth was/is known as "Cow Town" as well as "Where The West Begins".
-Downtown is only a long bridge walk over parks & a fork of the Trinity River from the Three Art Museums
...Downtown has been revitalized with lots of restaurants and bars built in red brick and gives you a feel of a town built between 1880-1910s (but not like BsAs).
...The Bass Concert Hall is something to behold from outside and probably pretty cool inside.
...Downtown is small and you could see most of what you'd want just walking around for 30 to 60 minutes.
FORT WORTH CONS:
-Maybe TOO Small
-Mainly 3 museums and an Old West area (the Ft. Worth Stockyards)
-Might feel like a visit to Montevideo (or smaller) rather than a visit to Buenos Aires.
-Not sure if there is a train/rail that goes from the airport to Downtown Fort Worth.
I admittedly don't know as much about Fort Worth, especially their downtown, as Dallas, but I also feel like the times I've driven around there in the past couple of years, I didn't feel like I missed anything after driving around for 10-15 minutes.