I like convention #2 - in researching this topic, and finding this question before posting my own, I ran into the issue where:
I am selecting * from a table with a large number of columns and joining it to a second table that similarly has a large number of columns. Both tables have an "id" column as the primary key, and that means I have to specifically pick out every column (as far as I know) in order to make those two values unique in the result, i.e.:
SELECT table1.id AS parent_id, table2.id AS child_id
Though using convention #2 means I will still have some columns in the result with the same name, I can now specify which id I need (parent or child) and, as Steven Huwig suggested, the USING
statement simplifies things further.