From personal experience there is a difference and it is a big difference.
They have seen evidence that these diets can retool the body to more readily use fat as an energy substrate. While this doesn't translate to performance gains, it can mean that on a multi-hour/multi-day effort that a self-supported athlete might need to have a bit less food in their packs as well as foods with a higher proportion of fat that are lighter. Lighter pack = faster athlete.
But...even low intensity exercise over long duration is going to result in the recruitment of FTa/FTb muscle fibers that run almost exclusively by glycolyis. So an athlete counting on fat to be the primary energy substrate has be really highly trained, practiced, and know their pacing thresholds really well to keep the recruitment of those muscle fibers to a minimum.
Best paper I know of on the subject is this one: https://static1.squarespace.com/static/55b7ffebe4b0568a75e33...
Best book I know of on long-duration effort is this one: https://www.amazon.com/Training-New-Alpinism-Climber-Athlete...
I follow TFTNA (Training for the New Alpinism) and Uphill Athlete (Steve/Scott's new book) training regiments that Parent mentions.
They do talk about retooling your body to use fat reserves more than carbs. While I'm sure the evidence shows that keto diet might make this switch faster and easier, someone on a non-keto diet (carb based) can also do this.
My other very favorite resource is Shawn Bearden's Science of Ultra podcast, which is where I learned of the research paper I linked in my first post. Here's the one on fat adaptation: https://www.scienceofultra.com/podcasts/19 . He has lots of pretty hardcore exercise scientists and researchers on. It's one of my favorite things to listen to while grinding up a hill. :)
I'm not saying my personal experience should be considered universal, that'd be foolish. Just recounting that.
But it makes sense given how metabolizing fat and metabolizing sugar works. Insulin response, etc.
Have you tried? I always run before eating (not as part of a regimen, it's just convenient), as I expect many do. And my diet is closer to inverse-keto than keto.
I think that your comment falls into the noise category and is undesirable because of that. If you had explained personal experiences to show how you reached your conclusion, It think you would get a better reaction. If you also showed how other possibilities could be rules out, then I think people would find it very interesting and you would get many up votes.
Also, looking at comments, often I see only upvote and no downvote button. Why is that?
You should absolutely train in a glycogen depleted state just so you will know what it feels like and can deal with it. But it's not how you would ever start a race.
In the marathon distance or shorter, being fat adapted would be a bad thing, as you couldn't train at upper capacities. But where you are running purely aerobically for very long periods of time (12+ hours), this may be an advantage.
The secondary (or even primary) advantage would be a low carb or ketogenic diet is that it is anti-inflammatory. People who run ultra distances do huge volumes of training, and it may be enabled by a lack of inflammation.
I successfully completed a marathon 3 months after reading his book after having never run more than 3 miles in my life. (Stu Mittleman - Slow Burn)