I have flown Lufthansa business class many times from Chicago to Frankfurt. I also made the same trip via American Airlines. Although I'm generally an AA customer (have 880,000 miles lifetime), I preferred Lufthansa for this trip. The seats seemed roomier, I preferred the in-flight entertainment configuration and the food seemed better. Most of my colleagues agreed with me. The flight crew was much more "businesslike" on Lufthansa, but that was fine for me.