It's different from AllAdvantage with the addition of market mechanisms to correctly price the attention consumed by ads.
That's why users get tokens for viewing, why users can turn the ads off entirely, and why the tokens are tradeable on exchanges. It creates a built-in feedback mechanism. If BAT is priced too low, then everybody will opt out of ads (because it won't be worth it to them), very little BAT will be available on the market, and advertisers will have to bid up the price of BAT to run their ads. If BAT is priced too high, there will be excess ad inventory, no advertisers will buy in, and the price of BAT will fall until it reaches an equilibrium.
AllAdvantage.com failed in a large part because they mispriced the rebates going back to users. They burned through all their VC cash, didn't provide enough value to advertisers, and went out of business. Brave avoids that by letting the market make the pricing decisions.
This is something that couldn't have been done at all before cryptocurrencies, which is what makes this project somewhat interesting.