In fact Kid and Law technically didn't beat Big Mom at all. She took several bombs in the head. Throughout the fight she tanked Kid and Law's ultimate attacks. She was still quite nerfed by not using her Advanced Kings Haki.
On the other hand, special mention to Trafalgar D Water Law, I take my hat off to him! I did an excellent performance against Big Mom with his awakening. His ultimate attack is exceptional, he perfectly masters his OP OP nomi.
Kid on the other hand is not at all impressed in the whole Wano / Onigashima arc, I find him borderline useless in this fight by the way. I find that Kid is just a Franky more with his robot, his magnetism otherwise well... That's all... Huge disappointment on the Kid case.
He didn't awaken any Advanced Kings Haki, didn't do anything crazy against Kaido, against Big Mom it's better but it sucks compared to Law. I don't know why people see him as a rival of Luffy, Luffy is far but far stronger than him in all areas. Luffy defeats Kid without even giving himself 50% at this point let's be clear