Local indexes can increase concurrency through multiple index access points, which reduces root-page contention.
You can place local nonclustered index subtrees (index partitions) on separate segments to increase I/O parallelism.
You can run reorg rebuild on a per-partition basis, reorganizing the local index sub-tree while minimizing the impact on other operations.
Global nonclustered indexes are better for covered scans than local indexes, especially for queries that need to fetch rows across partitions.