An apparatus comprises at least one processing device. The at least one processing device is configured to obtain storage-side performance information maintained by a storage system in conjunction with processing of input-output operations directed to the storage system by a host device over a network, to dynamically select a particular one of a plurality of distinct load balancing policies available in the host device based at least in part on the obtained storage-side performance information, and to apply the selected load balancing policy in directing additional input-output operations from the host device to the storage system. At least one of the load balancing policies comprises a storage cache aware load balancing policy that causes different ones of the input-output operations to be directed to different cache entities of the storage system based at least in part on cache-related performance metrics of the obtained storage-side performance information.