You don’t need to have one, but I chose to also have a Personalausweis.
I chose to get a Personalausweis to not continue to have to use my passport as an identity card (as I had to as a Briton). I got it a month or so after my passport, to ensure that the two documents do not have the same expiry date. It wasn’t essential or compulsory to have one, but the use outstrips the financial outlay (ca. EUR 65 when I applied in Summer 2018).