Interesting sale with Star Alliance between Chicago and Cairo. We usually don't recommend EgyptAir but since all flights are on Narrowbody planes, picking EgyptAir (Dry Airline) would give you a recliner seat versus EuroBusiness on Swiss/Lufthansa/Austrian. All flights are sold with LH codes in P class.
Lufthansa Business Class
EgyptAir Boeing 737 Business Class