My current favourite to CAI is Aegean (A3) via ATH, but I would always be starting in MUC or LIS. When BA flew a 787 to CAI, that was my favourite. I have tried Egyptair and it is quite acceptable if you can handle the awkward timings. Same for AF, though that is usually seriously expensive. LH/LX/OS I wouldn't go near unless the only option.

There is an exception though, and that is when after returning from CAI, I need to go to the US, as even with a stopover in Europe, BA's through pricing in J from CAI to the USA is still very reasonable making the mid-haul sector worth putting up with.