In soft Koi-Koi, YOUR multiplier increases by 1 each time you call Koi. Therefore if you call Koi a couple times in a round, your score can increase dramatically.
In hard Koi-Koi, YOUR OPPONENT's multiplier increases by 1 each time you call Koi. This essentially serves to discourage players from calling Koi and playing risky. HOWEVER: if your score increases to at least 7, it will be doubled (which doesn't happen in soft Koi). So there's a little bit of incentive to gamble and therefore increase your score, but not as much as in soft Koi.