Unfortunately, the 2 statements are functionally different.

The first will return the total count of distinct Departments. The second will return a recordset containing a count of employees in each department.

To get equivalent statements, you would need to do

SELECT COUNT(*) FROM
(
SELECT 1 FROM scott.emp GROUP BY deptno
)

Now, the difference between the statements becomes that the COUNT(DISTINCT) will use and index, assuming one exists, while the SELECT 1 will do a table scan.

In an OLTP environment, it is usually preferable to go after the index, because it is more likely that more of the index is in memory than the table itself. Plus, it takes up less memory. However, there are multiple other factors, including how much memory you have, how much of the table is usually in memory vs. how much of the index, what your block size is, how big your multi-block count is, etc. The best idea is to test it yourself, unfortunately. In either case, however, it should be very fast. A single table scan is usually nothing to fret over, although you will most likely be crowding other items out of the cache. If in doubt, the COUNT(DISTINCT) is probably your best bet.

HTH,

- Chris