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For stores that would like to begin accepting bitcoins, would Bitpay or BTCPayServer be a better choice? The first seems to act as an intermediary, whereas the second does not. How do they compare in reputation, reliability, merchant anonymity (no ID submission required), and ease of use?
Ideally, the transactions are entirely in Bitcoin, and not covered later by credit card.
Are there other, better services besides these two?
It's my highly subjective opinion, but if you're not a government organization, using a service provider like Bitpay is a terrible idea. Bitpay was known to create anti-privacy features, perform KYC, and even known to stop some payments from going to the recipient. Every time you use a payment processor who is the custodian for the funds you want to receive you're in danger of losing those funds. And on top of it, you pay for that.
BTCPay is feature-packed, not only for bitcoin (segwit addresses) but also for lightning network, connectivity to hardware wallets and much more. If you want to use any compliance suit on top, cool, but you don't have to. Also there are no fees for using an intermediary. You can create widgets and use it as a patreon page, webshop, or just monthly subscription. Setup is extremely easy and running it in a light version costs less than $10 per month.
