Emotionally, Ciel would be more detached. He would view relationships more as means to an end. His bond with Sebastian, for instance, would be less about a master - servant dynamic based on the contract for revenge, and more about power and mutual benefit. His view of morality would also change. What was once unacceptable as a human might now be a normal part of his behavior as a demon.
Ciel would likely become more cold - hearted. His experiences as a human, especially the trauma he endured, would be amplified by his new demonic nature. He might lose some of his remaining humanity, such as his sense of compassion.
His intelligence would be sharpened further. Demons are often depicted as cunning, and Ciel already was a very intelligent character. As a demon, he could use his wits in more devious ways. He would be more strategic in achieving his goals, whether it's revenge or something else. His physical abilities would also improve, which would change the way he approaches challenges.