Santander allows you to withdraw more money in comparison to the others, like R$2,500, however, it will charge you a greater fee. Bradesco allows you to withdraw more than R$1,000, but keep in mind that your bank will set a maximum limit per day as well. I know that Bradesco would charge the fee of 1% of withdrawn amount and sometimes +1 USD.
The worst bank to withdraw large amounts is Banco do Brasil, because it can give you only ~R$500 per day, which is nothing.
Itaú, from what I recall, also allows you to withdraw greater amounts, but the fees were similar to those of Santander.
As some other people said, it is not a good strategy to walk around with loads of cash because you may get mugged or robbed. Keep some money in your pocket, like R$200 per person, and leave the credit or debit card in the safe at your hotel (or hidden).
I would advise you to buy a special fanny pack we have here, which is hidden under your pants. We call it "porta dinheiro".We usually have it for Carnaval since you can't watch your pockets when the streets are full of people. It doesnt have much space but you can fit your passport and money. It would be good to keep a copy of your passport somewhere else too.