To be sure I understand:

For any given pareto-optimal solution, there is an equivalent utility-weighing that would give the same result. However, the weights will be different for each solution. (i.e. for any given X+Y = Z, I can say that X = Z-Y, but there are infinite possible combinations of values that match this pattern.)

Therefor, "find the correct pareto-optimal solution" is more efficient, since it always results in a solvable equation, whereas "find the correct utility weights" is under-specified since it doesn't tell you HOW to determine that?