In my opinion both biased and opinion favor one person or side over another.
However if you are biased over something, it seems like it was mandatory and you have grown up to believe one side of the argument over the other. For example with football, if a little boy’s father supported Manchester United and all his childhood he was brought up to think that Man United was the best football team out there, the chances he will support Man united are very high. So it has kind of been engraved into the child’s mind.
Whereas opinion is more of a personal thing that an individual has discovered through experience. Personal Opinions usually are discovered through age, as your brain gets more mature and you are able to think for your self.