Yoriichi is the strongest demon slayer to ever live. He was the most powerful user of the sun breathing and he was a prodigy.
Kokushibo is Yoriichi's older twin brother and is the upper moon 1. He is the creator and sole user of the moon-breathing style.
Yoriichi managed to almost defeat Muzan and he also faced his brother Kokushibo when was almost dead and would have defeated him had it not been for him dying of old age.
Kokushibo is the strongest demon, only second to Muzan, and has defeated many strong opponents. However, he would most definitely lose the battle against his twin.
Whilst Kokushibo developed a new breathing style, the moon breathing, it remained inferior to sun breathing.
Kokushibo developed 16 forms of moon breathing as a demon, but he would not be able to defeat his younger twin who happens to be a prodigy.
If Yoriichi was younger and not on the verge of death, he would have defeated his brother with ease. This alone proves his strength and power.
Therefore, in a battle between Kokushibo with his 16 forms of moon breathing style and Yoriichi in his prime, Kokushibo would lose miserably.