Russian and Ukrainian airspace is currently closed so neither airline will be flying over that. When I flew EVA from BKK to LHR just pre-pandemic, they skirted through Ukraine but did not fly over Afghanistan or Iraq, so I can't see TPE-ORD doing that.

As to airlines, the food on TK is great but the seat is from a previous generation. EVA is excellent IHMO on both counts (perhaps not quite as good food, but good nonetheless). However, I read somewhere recently that TK has scaled back its culinary offerings, but that may have been only mid-pandemic. I'm sure that the TK forum will reveal all. On a separate note, I'd love to visit the new IST airport and, most especially, the new lounge there which apparently is even more amazing than the old one, which is difficult to believe.