I won’t address the READ UNCOMMITTED argument, just your original question.
Yes, you need WITH(NOLOCK) on each table of the join. No, your queries are not the same.
Try this exercise. Begin a transaction and insert a row into table1 and table2. Don’t commit or rollback the transaction yet. At this point your first query will return successfully and include the uncommitted rows; your second query won’t return because table2 doesn’t have the WITH(NOLOCK) hint on it.