Apple and Google wallet have selected the most prevalent and widely accepted barcodes. Note that this is not a constraint of PassKit.
If future Wallet releases support other Barcode formats, PassKit will of course support.
The barcodes that Apple and Google currently support are:
Code128 (iOS9 +)
If you urgently need to use another type of Barcode (for example, if your existing scanning equipment only works with a certain format) you may consider uploading an image of a barcode into the Pass itself (eg as a Hero Image in a Loyalty Card). Of course this means you will not be able to have another image on the pass.