The end results of both products are roughly the same, but the integration process is wildly different.
Setting up Cloudflare's protection is as simple as toggling a series of switches on your domain's admin console. It's about as idiot-proof as it gets and all of the technical work is handled for you in the cloud. Anubis has to run on your server(s), which isn't necessarily a huge issue but can take a longer time to set up and occasionally be more difficult to maintain. Like with any self-hosted open-source project, there's also a greater risk of supply chain attacks, faulty patches, or misconfiguration, all of which could impact the security or reliability of your site. That being said, all of those drawbacks come with the huge perk of not paying for an external service and being downstream of the decisions that its owners make.
Ultimately, and here is where we stretch into my opinion, the choice between the two options is less technical and more personal/political. If you believe that Cloudflare's presence in virtually every corner of the internet is a problem and don't want to be beholden to their whims, then Anubis is the product for you. If you don't mind outsourcing your filtering, Cloudflare is fine. Some people also just don't have the time, skill, or desire to maintain a self-hosted solution, so they'll opt to "set and forget" the Cloudflare option.
If you're interested in learning about how Anubis works,
here's a fairly accessible article that covers that.
