NextDNS vs Cloudflare

For gaming, would Cloudflare’s DNS solution be better than NextDNS? (Less latency, etc) Depending on answers, I am planning to put the DNS server into Safing Portmaster

Not running away from the government, just don’t want excessive collection of my data from companies and other mysterious things.

DNS servers don’t really do much for your privacy. It’s just shifting your trust to a different provider.

See: DNS Resolvers - Privacy Guides

You might as well do gaming without a DNS service. The game devs are tracking you anyway. See point 1.

DNS latency doesn’t matter for gaming, your OS will make a DNS request for a game server once, and it will be kept in the cache for some time, so it pretty much doesn’t matter at all.
NextDNS is much better than Cloudflare, it has a much better privacy policy and it allows you to block known tracking domains.

If you are referring to WARP, it may help with reducing latency. However, it acts more like a VPN rather than just a DNS resolver.
Unlike a traditional VPN, WARP does not hide your IP from the sites that you’re visiting.