I think there is a big difference when one still ultimately requires a physical act in the end and one is all mental.
You can much more easily use the physicality of your surroundings to physically deny yourself the food than you can deny yourself anxious thoughts.
With eating there are 2 components to it, mental and physical, so you have more opportunities and more options and avenues to potentially control it.
The additional options to control it should IMO make it at least some amount easier to control in the end since some people may be able to take advantage of physical controls to limit themselves where that's not an option for anxiety.