A spokeswoman at Washington Mutual says that overall, the bank's strategy for product offerings and pricing is based on a variety of factors, including the type of channel (store, phone or online), market competition, product feature or enhancements, customer research and price.

"Our online channel provides us with an inexpensive way to acquire deposits, and we pass along some of those savings to our customers who like the convenience of opening CDs through Wamu.com," she says.

AmTrust Bank created AmTrust Direct to offer online products. The savings account online offers an annual percentage yield of 1.25 percent, with $500 required deposit to open it. Meanwhile, the in-branch offering, which requires $1,000 to open, offers 0.5 percent.

According to Julie Clemo Tutkovics, AmTrust's director of retail and business product management, the decision to create AmTrust Direct was made in order to reach customers nationally.

"Clearly, with a branch footprint in Ohio, Florida and Arizona, our recent retail strategies have included focusing on high-growth areas," she says. "AmTrust Direct seemed like a natural extension to provide great products and services to customers and prospects both around our branches but, just as importantly, to those where we do not have a physical presence."

Tutkovics says that "the pricing strategy certainly takes the national landscape into consideration, but we price our products based on what customer segment needs are, and typically online products tend to be a bit higher. We have seen a dramatic increase in our reach and now have customers across the country. That would not have been possible, in the short term, without a Web presence."

Not all banks offer different yields online

Not every bank has to compete on number of deposits, or rate, according to McBride. "The higher online yields reflect the institution's desire to attract deposits. Some banks are swimming in deposits because they have a branch on every corner."

For example, Bank of America offers the same APY and minimum amount to open for online and in-branch on their savings (0.10 percent) and money market accounts (0.90 percent), as well as the one-year CD (1.25 percent).

Bert Ely, of Ely & Co., an independent bank consultant, says that banks that offer in-branch and online banking have to be careful not to cannibalize their in-branch business. The online offerings bring in more customers that might not otherwise bank with them, but they are paying a higher yield for that money. So if the branch customers flock to the online products, the banks end up paying a high yield, plus a high cost to attract them through the branch business.

"It's a dilemma for banks," Ely says. "They don't want to compete against themselves."