I go back and forth on this question. I ALWAYS travel with my Apple Watch. It's on my wrist in the airports and if I'm working out. I'll frequently double-wrist if I think I'm going to need it. For instance, was pretty high up on my last outing - over 10K ft at times without a lot of time to acclimate, so i wanted to watch my O2. ( which was fine).
Usually I bring : 2 to 3 watches: 1. My Apple Watch; 2. Something mechanical for the flight usually set to the destination's timezone that I put on in-flight to help with jet-lag ( this really does help); 3. And if I"m bringing a third, it's because it fits the occasion in some way watch #2 won't always. Usually that third choice is a green Seamaster 300M since the green dial is so changeable in different lights. Or my strap-monster Panerai. Or a dress watch ( if either of those are watch #2 and I need a dressier piece). But on my last trip I brought my Speedy on the new bracelet w/the quick adjust. I was going to some patriotic sites in the west ( Mt. Rushmore, Yellowstone, Crazy Horse, etc. ) and I wanted to have it with me for reasons I can't exactly explain.