I remember in the Caroll Spinney Story that Emilio Delgado said he actually stormed into the control room to reprimand Jon Stone for lashing out at Caroll Spinney simply for flubbing a line, which escalated into a heated dispute, adding that, "Luis is very protective of Big Bird." Unfortunately, I can't really think of too many occasions off the top of my head where Big Bird had any big moments with Luis, but it's a nice thought that Luis would have sort of a paternal instinct towards Big Bird.
I do remember Luis took on certain responsibilities during the hurricane to help Big Bird, such as putting the construction doors back up and reconnecting his telephone. Also, I've made the observation that, like Snuffy, Luis tends to call him just "Bird" on some occasions.
Alan seems to have really good chemistry with many of the Muppets as well, which is one of the reasons why I've really enjoyed him as a castmember since they introduced him in 1998. I remember reading in the 40 Years book that his screen test included consoling Big Bird and helping him find his missing Radar, and that it went really well.
I remember a few occasions where Gordon would become easily flustered with Ernie much like Bert, such as an occasion where Ernie asked Gordon to ducky sit for Rubber Ducky, or when Ernie was sleeping over in Big Bird's nest, and Ernie kept calling out to him throughout the night.