Don’t be so hard on yourself. Maybe you really don’t play favorites and he just feels that way because of his nature. Try speaking with him and tell him you that you love and care about him as much as his brother. Tell them they are both “the best”. Make it clear to him that if he ever feels you are giving more attention to his brother it is because you feel that his brother needs more help at the time, and you would more than happily do the same for him when he needs extra attention.
However, maybe he is correct in his complaint, and you actually show favoritism to his sibling. I realize that your different “feelings” for your different children are hard to control, but you can certainly make an effort in how you express your feelings in the way you relate to your children.
It is extremely important not to show any sign of favoritism towards one child over another. This rule in raising a family is found in our Jewish teachings. When Jacob gave his son Joseph a “coat of many colors" it caused jealousy with Joseph’s brothers. As a result of this jealousy, which had other reasons as well, the brothers nearly killed Joseph. They ended up selling him into slavery, and he was eventually taken to Egypt.
In the words of the Talmud: Rav said that a person should never single out one child among his other children, for on account of the small weight of silk that Jacob gave Joseph more than he gave the other sons (Gen. 37:3), his brothers became jealous of Joseph and the matter resulted in the Israelites’ descent into Egypt (Tractate Shabbat 10b).
I really doubt anything even remotely close to this would happen in your situation! However, it is worthwhile doing what is possible to build and maintain family harmony, mutual love of all siblings and to avoid rivalry and jealousy. I suggest telling and showing both of them how much you care for each one to the maximum.