With the caveat that I’m neither a chemist nor a chef, I see these as serving different purposes.
Sodium citrate acts as an emulsifier, primarily (at least in the KF recipes) for making a smooth cheese sauce. I’ve used it with a variety of cheeses, and have generally had great results, though like xanthan gum, it can take a while to come together. I do find that it’s pretty forgiving, unlike xanthan gum, so if you get the proportions wrong with sodium citrate, you can usually add more cheese, or more water, to get the consistency you want.
Xanthan gum is more for thickening, and the way I typically use it is to take pan drippings, add some fat and more liquid if needed (melted butter, heavy cream, etc.), and use my stick mixer to blend them up, while simmering to cook the mixture down to thicken naturally. Once fully blended, I may add xanthan gum to get a little more thickness while preserving the volume of the liquid.
The one place I can potentially see sodium citrate being useful for a gravy is in preventing separation. I usually find that even a well-blended gravy can suffer separation once I refrigerate the leftovers. But I’ve never tried using sodium citrate this way, so I can’t vouch for whether it would work, or if there would be undesirable side effects. I may give it a try the next time I do gravy.