So... What exactly makes Light better than Higuchi?
Rem was slagging off Higuchi to Misa, though she didn't approve of Light much either she seemed to think of Higuchi as worse.
Higuchi got the notebook and used it to advance in his company to a higher position then to eliminate rivals of the Yotsuba group. He wanted to be Kira and use the notebook to obtain money and power. He didn't seem to care much about the criminals he was killing. Must have just been scared of Rem or something so went along with what she had told him to do.
Light on the other hand well the first two names he wrote were selfless and for a good cause. After that killing as many criminals in jail as he could, that was going a bit too far. Also killing people who said he was evil, does a world run by Kira not allow free speech? But anyway did he really care about punishing people who had done wrong? No, he did it because he wanted to create a new world and be as he called it, "God of the New World." In theory he was just doing what Higuchi had tried only on a much bigger scale. Higuchi wanted to advance his position to a top class businessman while Light wanted to advance to being seen as a god.