As someone who has (1) quit smoking, and was definitely an addict to it; and (2) dropped 40 pounds and kept it off for some years (from 230-and-growing to 190 - I’m a 6’ guy in his 40s), I’ll relate my, entirely subjective, view of the matter.
To me, the two are different, but they are more alike than they are different. I will explain how.
In the case of both smoking and over-eating, what really matters isn’t the mechanism of “quitting” - in my case, with smokes, it was cold turkey - as the making of significant lifestyle changes. It isn’t enough to say “well, I’m not smoking, that is that”. You gotta change your pattern of behaviour and activity, because, for me at least, my former patterns included having a smoke.
This is pretty burdensome, because having a smoke was tied into a lot of things I found enjoyable - from going out for a drink with friends, to taking a break from work, even sitting on the dock at the cottage and watching the sun set. True, I could (and now do) enjoy all of those things without a smoke, but my pattern of behaviour was to smoke doing them.
Eating was much the same deal. Part of the pattern of activity I enjoyed involved eating, or at least consuming calories - going to family events and birthday parties, going out for a drink, even going to a movie involved (traditionally) getting buttered popcorn and a pop.
It took a great deal of effort and inconvenience to arrange my activities so that I could avoid patterns in which smoking and eating were part of the pattern.
Eating is different in that of course aside from the purely negative activity of arranging one’s habits and routines to avoid eating “recreationally”, you have to go that extra mile to positively arrange one’s activities to eat sensibly.
However, the big difficulty in both cases is really the same - that it can be really, really tough to arrange your existing life to accomodate your new reality. Your smoking and drinking buddies you may not have as much in common with, if you don’t smoke and only drink moderately. You don’t take smoke breaks at work. Your in-laws have arranged a traditional holiday feast, and you don’t partake above a salad and some chicken breast - they are pissed. You go to a movie and don’t have popcorn. These are little things, but their cumulative effect can be harsh, because along with giving up the addictions and bad habits which are doing you harm, it can seem like you are giving up on the enjoyable small change of life.
The key, of course, is to replace the former habits with new ones which are also enjoyable but are not centred on the self-harming behaviours. So in reality, both quitting smoking - which appears a totally passive decision (that is, you just stop) and quitting over-eating - which does not, both really require some positive action to succeed - the positive action of replacing old habits and patterns with new.
At least, that’s been my experience. Others may find it different.