Brave is based on Chrome, whereas Cliqz is based on Firefox (just to be precise). Note that ownership of code is not the same of ownership of a service... if Brave is depending on Google services, then you would be right (what happens with the [meta]searchers. But the code is open, and can be forked at will (there are some caveats to that claim, licences, internal APIs, etc.)
You can collect data from users and still do not compromise their privacy, it's how you do it that matters, becomes a design requirement. Collecting a url visited, can lead to build a user history (privacy hazard) or not. It's an design choice. The whole mantra that data!=privacy is doing a lot of damage (for anyone curios we did publish plenty of material on the topic, https://0x65.dev/blog/2019-12-02/is-data-collection-evil.htm...)
You can collect data from users and still do not compromise their privacy, it's how you do it that matters, becomes a design requirement. Collecting a url visited, can lead to build a user history (privacy hazard) or not. It's an design choice. The whole mantra that data!=privacy is doing a lot of damage (for anyone curios we did publish plenty of material on the topic, https://0x65.dev/blog/2019-12-02/is-data-collection-evil.htm...)