When we tour on our tandem, we generally use huge, BMX platform pedals. Sometimes the captain will put some toe-clips on hers, but I usually don't. We spend a lot of our time on unpaved fire roads to avoid traffic, so it is nice to be able to get both, actually all four, feet off the pedals and stably on the ground at the drop of a hat. I'm a little restricted for footwear because of my size 51 shoe size, so I don't know what I would use if I had a more normal foot.
On my half-bike, I use Look pedals and a road shoe. I'm not walking except into a grocery store and I would bring a pair of lightweight camp shoes anyway, so there is no penalty for riding in road shoes. Also, I tend to cover 100-200 miles per day when I tour on a single, so I want my feet to be happy.