Both have ads baked in. Brave turns them off by default but tries to get you to turn them on and gives you fractions of a cent in crypto if you do. Mozilla has them on by default.
What ads does Firefox have?
Both have bundled things in their browser. Brave it was their VPN and affiliate link scandal. Mozilla was plugins like the Mr Robot plugin and changing people’s search engines to Bing without their consent when negotiating with Google.
The Mr. Robot plugin stopped being auto-installed a day after people complained about it back in 2017 (7 years ago), and I don't think this ever happened again, while Brave still does its thing to this day (to my knowledge), I haven't been able to find any info on that second point.
Both have made fringe political donations
Which fringe political donations has Mozilla made?
Forgot about the home screen sponsored stuff since it's so easy to disable it, as for sponsored search results, I've only been able to find stuff about sponsored search suggestions, minor detail. Mozilla suggest
I've not been able to find much info on this, the only thing I found was a member's only blog post by luduke (who I don't trus), so I can't say much about this.