I think Y2K had more practical impact across the business world. There was genuine fear that it could cause an actual apocalypse with all major computerized systems failing, medical machines killing people, banks being affected and all money and debts disappearing overnight.
It wasn't that bad, because people took it seriously. But there were still tons of practical systems affected and billions of corporate dollars associated with fixing it.
So when you say "biggest mess up" you gotta define specific qualifiers. Because Meltdown/Specter is going to be solved by simply... buying a new CPU. (And retrofitting the old ones). So it consist of mostly a patch.
A BIG important patch, granted. But it's still just a patch. But some ATM's aren't going to start spewing money like they did on Y2K.