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Be careful about lists posted by random links. The website you shared puts bitpay as the top option for a crypto payment processor, and with my little research on it, that cannot be further from the truth and I would advise that you avoid using them.
You would be better off searching here on the forum and following discussions centered around that topic.
About the better option, as mentioned above, it depends on what you intend to achieve through the addition of crypto as a payment option;
• If you're scared of the volatility of Bitcoin, a payment processor should be the leading option,
• If you're looking to stack up your portfolio, receiving crypto like Bitcoin through the lightening network to your personal wallet is the better option.