I'm not an expert on licenses, but from my own understanding of AGPL, I'm not sure why Parity and/or API Copyleft would give better protection against SaaS corp

I'm not an expert on licenses, but from my own understanding of AGPL, I'm not sure why Parity and/or API Copyleft would give better protection against SaaS corporations. Would you be able to explain why AGPL is not as good as the two licenses you named?