An attractive rate may only apply to part of the balance. To compare two accounts, work out the interest on each tier and divide the total by all the money you want to deposit.
An example with numbers
Say you keep $20,000 for a year. Account A pays 4% only on the first $5,000 and nothing on the rest: it earns $200. Account B pays 3% on everything: it earns $600. The example leaves out compounding, fees and taxes.
Try it with your numbers
Divide A's interest by the $20,000 deposited. Compare that effective 1% on your balance with the second offer.
Example figures for learning purposes. They are not a recommendation and do not replace professional advice.