't have to really think about the string size in the matter of how much energy it takes to move, because the hammer size does that. Look at it of more the size, or the smaller object is easier to move, so moves faster, running out of energy first.(don't worry about energy to actually move it, as the hammer increases with string size, artificially making the amount of energy needed to move the string is the same, however not the same amount of time)
Sorry if it's hard to understand, it makes clear sense in my mind, kind of hard, and a bit abstract to explain it, and the way I think about it.
Hope that is a quick simple to the point answer.