BTCPay has more "merchant" oriented features, like generating a new address for each transaction and keeping track of them so that, for example, you can see who has paid and who hasn't. The obvious application for this is a web store, where you need to wait for payment before shipping a product; but, it could also be used in patronage scenarios where paying patrons get access to exclusive content.

Right off the bat I imagine that there is a more reliable income stream with some of the patronage sites that exist, whereas with a Bitcoin address in the footer, you are only relying on a single one-time donation.

The goal of BTCPay server is to use the Lightning Network for Bitcoin payments, which only generates single-use payment requests. Also important to point out that LN will not be functional for years, so...