A poisoned Pokemon looses 1/8 hp per turn
A badly poisoned Pokemon looses 1/16 hp on the first turn, and the amount lost increases by 1/16 each turn
So lets see:
Turn 1:
Poison: 1/8 hp loss
Badly poisoned: 1/16 loss
Turn 2:
Poison 1/4 loss
Badly poisoned: 3/16 loss
Turn 3:
Poison: 3/8 loss
Bad poison: 3/8 loss
Turn 4:
Poison: 1/2 loss
Bad poison: 5/8 loss
So, by the third turn, they tie, and bad poison surpasses at the fourth turn.