A "sort merge" join is performed by sorting the two data sets to be joined according to the join keys and then merging them together. The merge is very cheap, but the sort can be prohibitively expensive especially if the sort spills to disk. The cost of the sort can be lowered if one of the data sets can be accessed in sorted order via an index, although accessing a high proportion of blocks of a table via an index scan can also be very expensive in comparison to a full table scan.
A hash join is performed by hashing one data set into memory based on join columns and reading the other one and probing the hash table for matches. The hash join is very low cost when the hash table can be held entirely in memory, with the total cost amounting to very little more than the cost of reading the data sets. The cost rises if the hash table has to be spilled to disk in a one-pass sort, and rises considerably for a multipass sort.
(In pre-10g, outer joins from a large to a small table were problematic performance-wise, as the optimiser could not resolve the need to access the smaller table first for a hash join, but the larger table first for an outer join. Consequently hash joins were not available in this situation).
The cost of a hash join can be reduced by partitioning both tables on the join key(s). This allows the optimiser to infer that rows from a partition in one table will only find a match in a particular partition of the other table, and for tables having n partitions the hash join is executed as n independent hash joins. This has the following effects:
You should note that hash joins can only be used for equi-joins, but merge joins are more flexible.
In general, if you are joining large amounts of data in an equi-join then a hash join is going to be a better bet.
This topic is very well covered in the documentation.
http://download.oracle.com/docs/cd/B28359_01/server.111/b28274/optimops.htm#i51523
12.1 docs: https://docs.oracle.com/database/121/TGSQL/tgsql_join.htm