Hash option is only for performance and not for the conditional functionality. The hash option in Horizontal Partitioning does not allow the use of column conditions. In case of latter you can send subset of data to various targets or tables based on some logical operator. Thus for the Horizontal Partitioning using column conditions and using hash operator are mutually exclusive.
Here are the differences between the two options:
1. The hash option involves every row of the source table whereas the conditional option may involve a subset of the rows for replication purpose.
2. The hash option is only invoked for performance reasons whereas the conditional option is for filtering of the rows to be replicated.
3. The hash option will require memory resources on target as the table in question will spawn multiple Post queues on target, the number of such queues will depend on how user configures the hash option. The conditional option on the other hand will not create additional Post queues on target.
4. Table can't be Compared / Repaired if it is Hash partitioned where as the conditional option supports Compare (or Repair).