Custom tables, to give the short version, make scaling a lot easier. You can structure tables to be catered to your application, versus shoehorning something into the posts table. Pippin uses the example for orders on Apply Filters, which he regrets making a CPT. But making tables isn't very easy, and you have to consider a lot of different stuff.
Pippin Williamson has a second part out in his series on creating an API for custom database tables. He and Brad also talked about custom tables, when to use them, how to use them, and things to look out for on the newest episode of Apply Filters. This is a very informative conversation, and it's really interesting to see Pippin (one of many to do this) go full circle on custom tables.