Is Query of Queries faster than multiple WHERE criteria?

If I need a recordset based on two table column fields (let's say firstName and lastName), is it better to run one query with a WHERE firstName = x AND lastName = y, or is it better to query of queries and find all records with a specified firstName, and then query that query to filter only records with a specified last name?  Which is the better/faster method?

<cfquery name="somequery" datasource="someds">

SELECT *

FROM sometable

WHERE firstName = 'John' AND lastName = 'Smith'

</cfquery>

or....

<cfquery name="somequery" datasource="someds">

SELECT *

FROM sometable

WHERE firstName = 'John'

</cfquery>

<cfquery name="somequery2" dbtype="query">

SELECT *

FROM somequery

WHERE lastName = 'Smith'

</cfquery>