As you might expect, the answer is that big banks don't have to offer much. According to this CNNMoney.com
By the mere virtue of their size and the convenience they offer to consumers, large banks have managed to attract deposits with little trouble in recent months.
Unlike the big banks, the small banks have to keep their rates competitive to retain and build deposits. The article mentioned one small bank that I've covered: Country Bank in MA. Their high rates have been successful in attracting deposits. According to the article, deposits have grown 10% this year.