The simple answer is no. Both products do help supply electricity that homeowners can use for any electrical device in their home—from air conditioning to microwaves.
Home backup generators, when properly installed and wired to the home’s circuitry, can provide adequate wattage to the home to run all selected circuits simultaneously, with the output they require. Home appliances draw different amounts of power when they operate—a microwave may require 1000 watts of power, and a refrigerator may require 500 to 750 watts to operate. Generators steadily produce their power, fully supporting all circuits they are wired to.
Home batteries cannot supply the full wattage of the power they may hold all at once. For example, a battery that may be charged with up to 10 kWh of energy, in order to protect the longevity of the battery, cannot dispense its power at more than a 2 kilowatts-per-hour rate. This means that only certain appliances would be able to draw power at any given time from the battery. In a power outage, the battery could support only limited items in a home at one time (e.g., just the refrigerator, but not the furnace).