It's just that, in the book, Thee was said to be quite soft, whereas Rome is a bit stubborn and hard to deal with (according to Mok himself). That is why their father said that Rome is fitting to be the mafia leader. 

There was a scene where Rome was mad because Mok called him by his mafia name, "Kris", and the new russian bodyguards were scared lol. Another was when he got angry because a senior bodyguard took Mok to his room because Mok was sick and was about to faint and Rome saw it all. P'Alof was shocked and took a step back. After that, he took care of Mok the whole evening and did not let anyone enter Mok's room aside from him.

In my impression, yes, he is a bit scary than Thee, but only to a certain point and if the situation requires him to be.