train: print out your timetable:

http://wapps.sbb.ch/hafasd/dhafas1.htm

type in the Stations: "Frankfurt Flughafen" and "Zürich" and the date and desired departure or arrival time.

train advantages: more room, more relaxation, more sightseeing (the Rhine!), and in Frankfurt you start in the airport, and in Zurich the main-station is in the middle of everything. No or just low taxi fares in Zurich (from the airport to a hotel in Zurich you are likely to pay more than $30 each way). Cheaper than planes. Much better chances of beiing on-time.

train disadvantage: bagagge-handling, no miles

neutral: time

(there is a direct AA flight from Chicago O'Hare to Zurich, also SR, and very likely SR/AA will codeshare AA & SR-flights to ZRH starting this spring - they are in "finalizing" talks just now).