Sorry, but Over was the strongest villain before Shigaraki got physically enhanced and AfO. Not even Giganto could beat Overhaul, he would get disintegrated. That's why he had his quirk taken away.
Destro Jr has a better and stronger organisation behind him, more political power, financial powers, more men, and quality wise they were better.
So Destro threat was a lot higher than Overhaul ones. Overhaul had Eri and erasing quirk bullets that made him dangerous.
MLA vs 8 precepts : the MLA pinpoint where are the Precepts and destroy them. Or they just call the heroes to beat Overhaul.
Now chief vs Chief : Destro JR is a highly skilled individual who trained a lot and has mastered his quirk. Overhaul is good too but he will need to merge to have a chance to do something. If he doesn't become mega kaiju Destro crushs him.
Destro crushed Shiggy in the beginning and shiggy was fast, like really fast. And Destro has top intel so he will know Chisaki powers. I don't think Overhaul has that much of a chance here. Army vs Army or 1 vs 1.