Those are all tough races. I still go with Barkley being the toughest since it's mostly scrambling in rough eastern Tennessee mountains avoiding nearly anything resembling a trail, except for a power line covered with briars. Throw in the 60 hours to finish it and it's almost unfathomable. You have almost no margin for error and it's very easy to get lost. No GPS allowed, just a hand drawn map you made in the few days before the race. The low finish rate is also very indicative, though many of the best ultra runners skip it as just being a foolish race. I had met the Belgian guy who set the AT speed record and he looked far better at ~800 miles in near my house than either of the elite ultrarunners who I have also seen on their now former speed records. And Karel did not finish Barkley last year.
I know less of Marathon des Sables, though my understanding is that it's a staged race so you have lots of recovering and pampering. 4 times a Barkley finisher will get back to camp, and if they have any time for sleep at all it is less than an hour.
Badwater is also very tough. But you have a crew vehicle accessible the whole way, and many have an ice chest to soak in when it gets bad. They also moved the start in Death Valley to sundown to avoid the early meltdown in the hottest part of the day in the hottest part of the US. I have a friend of mine who won that twice, and set the record until it was beat last year. There is a * for both of them because of the new start time but they both smashed old times. My friend also holds the fastest time on foot across the US (SF to NY), on roads.
Now of course I could hold the "lap around my house" race with a time limit of 5 seconds, and that would be the toughest race in the world if you are solely talking about finish rates, but that's silly. Barkley is possible. Just not easy. The only "easy" thing about it is that most people time out in the first loop or two, so they aren't put in the danger zone like someone slogging through Badwater, where you can see it's possible to finish, but it's just hot misery. I wouldn't run any of them because I hate heat. If I had to pick one, I'd have to do more research but I'd lean towards MdS.
David H. is my friend who finished Barkley. He's a legend, a character, and a good guy. Pete K is my friend who does Badwater. If you can't figure that out, PM me. No special reason not to name them, but I guess I maybe don't like worlds to collide.
Oh yeah, it's easy to get me talking about running, and especially different races. The tough part is to get me to shut up. And not that it was a requirement, but my GF loves to talk about these too. She says she would love a shot at Barkley, and she would likely finish more loops than me (probably 1-0 or 2-1). We are going to try to get her in the Barkley Fall Classic (basically one loop of the course) instead.