If one or more of your children think you play favorites, then you may as well accept it: you do.
Whether you have a "favorite" child is strictly in the eyes of the little beholders in question. To a child, a parent who treats different children differently is playing favorites. If, for example, you allow your 15-year-old to stay out until 10:30 on weekend nights, but insist that your 13-year-old be in by 9:00, you will undoubtedly be accused of being unfair.
Likewise, if your 15-year-old notices that his younger sibling is not required -- as he was at that age -- to mow the lawn every Saturday morning, again you are playing favorites. No matter that the 13-year-old can't tell the difference between flower seedlings and grass. Your older child will no doubt take this as a personal affront, and no explanation will convince him otherwise.
Defuse the Argument by Agreeing. The best thing to do when you stand accused of prejudice is to simply agree -- and a little humor never hurts. On the matter of mowing the lawn, simply tell your 15-year-old that scientists have discovered a connection between mowing the lawn and high intelligence. You are simply making sure, therefore, that he has a lifetime advantage over his younger sibling. In other words, he must mow the lawn because he's your favorite!
In short, the less seriously you take these complaints, the less mileage the children will get from them. Likewise, the moment you start trying to treat children fairly, the more tangled up you will become.
Don't Try to Make Things Even-Steven. The more you try to be fair by spending roughly the same amount of money and time with each of your children, chances are good that your children will carp that much more about how unfair you are being.
It may be hard to see while your children are still young, but nearly every time one of them accuses you of "liking" the other one better, the accusation may be right on target -- in a way. You may like your son for his sensitivity, his willingness to take risks, and his ability to make friends. On the other hand, you like your daughter for her madcap sense of humor, her insight into human nature, and her flights of creativity.
Unfortunately, your children, being children, fail to see that although assigned differently, your affections are balanced. So, when you laugh at one of your daughter's impressions, your son will accuse you of thinking she was "funnier." Translate: You "like" her better. And vice versa for anything your son does well. Fortunately, these wounds are short-lived, as long as you don't turn minor differences like a big deal.
Get Past it and Move On. The bottom line: You, like all parents, play favorites. Stop denying it! Accept, admit, relax. Stop trying to explain yourself. Above all else, stop taking your children so seriously. If you're praising them both, loving them both, and caring for both of them uniquely but in similar quantities, you're doing fine.