The key difference is that ad blockers such as Eyeo (Adblock Plus) often demand that publishers pay them to have their sites whitelisted. In other words, Eyeo just collects a fee (bribe) from publishers who want to circumvent the ad blocking. In most other contexts, one might refer to this system as a rampantly corrupt one.
Meanwhile, Brave suppresses all third party ads, and allows users to opt in to see BAT Ads. If you choose to receive ads, you get paid for the ads viewed. Users can also choose to use the tokens earned to tip websites, and most likely, in future iterations also to pay for goods, services or subscriptions using the BAT tokens. In other words, Brave could harbor an entire ecosystem whereby the power and the means lie more in the hands of the user (rather than in the hands of a few tech oligopolies and third parties).
Meanwhile, extensions such as AdBlock Plus have their ad replacement enabled by default when a user installs the extension. They may call the ads they let through “Acceptable Ads”, but this is grossly misleading. What deems an ad ‘acceptable’ is largely whether the publisher pays Adblock the bribe required in order to let its ads run.