I like using this function for audit tables. If you have an application that allows users to add, edit, and delete, you can use this method to keep track of the changes performed by those users. Nice if you are asked to provide information such as who updated the record and what was changed.
Honestly these days for auditting purposes, I prefer CDC.
I just started using OUTPUT recently versus running multiple statements to put data in one table and then remove it from another one. I haven't looked into CDC yet. OUTPUT is pretty easy to implement and understand (at least for me).
Actually, CDC is even easier, and it's based on SQL Server replication technology instead of trigger-ish based technology that OUTPUT does. The CDC system reads the Transaction log and records changes, it has a much lower impact on transactions.
That said, I use OUTPUT for things, just not auditting anymore.