Brave's primary customers are advertisers. While this is not evidence in itself, it is certainly something to be wary of.
Which FAQ?
This appears to be the only FAQ that mentions anonymized data:
> Will Brave sell user data to advertisers?
>
> We do not have access to identifiable user data. The anonymized aggregated ad campaign related data we do collect is used for accounting and reporting, but this data cannot be mapped back to devices or user identities of any kind. Learn more
If you follow the "Learn more" link it says:
> If you switch on Brave Rewards and switch on ads (in Rewards settings) you will see ad notifications, and will receive BAT to reward you for viewing these ads.
It seems like it's off by default?
So like Firefox?
Do they collect your history? No. Then good
Firefox does too.