Law basically did nothing to Big Mom.
He made her vomit a bit of blood (with an internal attack), not even lose balance, with his (up to today) strongest attack, used from behind when she was focused on another opponent.
For example, Zoro's Tatsumaki slashed Kaido and made him vomit blood (even if it was an external attack!) and Tatsumaki is far, far, far from being Zoro's strongest attack.
To have a comparison, Law's Gamma Knife couldn't even made Kaido vomit blood (and it was an internal attack).
Zoro's Ashura on Kaido really seems on another level.
It seems that Zoro (Ashura) > Law (awakening) = Zoro (Santoryu) > Law (other techniques)
After all, this was Law's reaction when he witnessed Zoro using Ashura against Kaido. And the conversation in this chapter proves that Law already had awakening at that time.
And that's not the reaction you have if you can do the same, let alone better.