The American revolution is a point in favor of Pitt in hindsight, he warned about that shit and no one listened to him.
The argument though(as far as I understand it) is supposed to be about what his contemporaries thought of him though, and it's pretty clear that Palmerston wins that battle.
It's really hard to compare since the time periods are so different. At the time of Palmerston, the British empire was at it's peak, and the loss of the American colonies seemed completely insignificant. At a time like that it's easy to be popular.