Which query is optimized
You could also write

SELECT Fname, Lname, Address 
FROM   department
JOIN   employee 
       ON employee.dno = department.dnumber
WHERE  department.Dname = 'Research';


which is equivalent to query two and can be a clearer form (see https://stackoverflow.com/questions/1599050/ansi-vs-non-ansi-sql-join-syntax for an answer that describes why the newer syntax is preferred). Most query optimisers will see this equivalence and perform the same operations for such a simple query, though for more complex queries this may not be the case (if there is a difference the JOIN variant is likely to be the better of the two).

Not that this is almost equivalent to the inner part of your first query, join syntax you have used is the older but equivalent one. As you are doing that in the inner query then just adding an extra filter in the outer one, a good query planner will see these queries as identical and run them exactly the same way. A bad query planner will have the engine run the inner query first then apply the extra filtering clause making it much less efficient depending on what indexes are present for it to use.

But this all depends on a few things that you should edit your question and tags to provide:


What database you are using as different query planners may not optimise the same way for a given query (add the database and version to the tags).
Also most database engines provide a way to read what the query planner is likely to do for a given query which case be useful in judging which option is most optimal - I'll not list how to do that in every database I know though, be specific about the database(s) you are working with and we can be more specific &amp; relevant about the answers we give.
The indexes present on the relevant tables (add the index and key definitions to the question text)


Note that if you run the second query and there are two rows in department where name='Research' then you are likely to get an error as the = operator can only work on one value each side. To list people in all departments with that name use IN instead. This may change the answer to which is most efficient.