the ISS is flying over my house tonight and I really would like to get a shot or two of it. I have at my disposal a 5D2 and a 7D, a 70-200 2.8 IS2 and a tripod.
Which of the cameras should I use? Is it best to go for IQ/ISO over reach?
Depends on what you are trying to capture - a trail or an image of the 357'x167' ISS at 230 miles. Google "photograph ISS" for some pointers. Here's a few good articles.
Trails need a long exposure with a wide/normal focal length.
Images of the ISS itself is another matter. NASA has a page about it http://www.nasa.gov/mission_pages/station/expeditions/expedition30/photographing_iss.html. The ISS will be pretty small even with a long telephoto lens. Even a telescope will not give much detail - http://www.apstas.com/astrotas/Sayers/PhotographingtheISS.html
Use the dimensional field of view calculator at http://www.tawbaware.com/maxlyons/calc.htm to determine the image dimensions. A 600mm lens on a FF camera has a 72864'x48576' field of view at 1214400', yielding an ISS image of 25px by 12px on the sensor. You would need a lens with a 120,000mm focal length to fill the frame of FF, or 75,000mm for APS-C.