Both could take each other out, but i would lean toward Briggs, he was bigger, probably with a better chin and faster hands.
I love Earnie, and this could be like his fight with Roy Williams, which he just barely won. I would pick him, though really it's 50\50.
I think I'd favor Shavers. Briggs failed to put away Botha and lost in most people's eyes during what was basically his peak. Maybe the older Briggs who beat Mercer and some scrubs would do better. He was more of a tank at that point and not permanently winded like when he fought Liakovich.
Shavers has a better chin than people credited him. He is known for having a glass jaw for his round knockout over Jerry Quarry and knockout loss over Stander. And it makes sense becuz they're not that big of a puncher to kayo anyone like that. BUT! later in his career, like every glass jaw boxers, he has start to learn how to take punches better and hold a tight high guard. He withstood the punches of Larry Holmes, Bernardo Mercado, Jeff Sims and even Ron Lyle. Although Mercado's and Sims's punching power are still unknown, but I at least think that they both might hit harder than guys like Briggs. So in conclusion, Shavers may have enough chin to withstand Briggs power and he has more than enough punching power to kill Briggs. Shavers by 4th or 5th round KO
Quarry beat Shavers by jumping on him early (albeit as a counterpuncher, and he did absorb punches to do it.) Briggs has the speed and experience jumping on people early that he could probably take Shavers out. Not a fight I'd bet on though.