Distibutional problem
We can consider the more general problem of makespan, in which we wish to partition the tasks into $m$ sets as evenly as possible (your case is $m=2$). We measure the quality of our solution using the maximum total sum of a set, which we wish to minimize. Finn and Horowitz showed that the locality gap for this problem is $2-2/(m+1)$. This means that a locally optimal solution has objective value larger by a factor of at most $2-2/(m+1)$, and moreover there are examples in which the ratio approaches $2-2/(m+1)$. In particular, local search doesn't always give the optimal solution.

For other local search algorithms for makespan, consult the survey of Schuurman and Vredeveld.