I can certainly understand both camps. In fact, I think I'm a little of column A, a little of column B, personally. I consider both the game, the situation and the child and then make my decision.
Colin is very competitive and, as the oldest, often beats Caleb, so there are times when I play hard and beat him. It helps him understand what it's like to lose, how to be a gracious loser, how to be a gracious winner, and how to have fun. But I don't want him to get discouraged, so I also let up and let him win sometimes.
Caleb is very emotional, so right now, while he's only three, I usually let his mood dictate the game. If he's well rested, well fed, and having a good time, I let Colin control their games. But if things might meltdown, I ask Colin to play with Caleb instead of against him, to take the role of older brother and coach.
This all seems to be working well for us so far. Of course, then there are the times when it's not even a question. Like to when James and Colin borrowed a wii video game system and broke out the bowling. Game 1 final score was Colin: 196 to James: 105. Colin got 5 strikes and 3 spares. And James really did give it his all. "You don't need to worry about whether or not to let your 5 year old win when they can actually beat you!"