u mean by using 12V input? It still step down to 5v.mayb just the battery can last longer
You need to understand the difference between a switching regulator and a linear regulator.
A linear regulator's input current is the same (actually slightly more) than the output current. It wastes as heat the difference between the input voltage * current and output voltage * current. Increasing the input voltage decreases efficiency.
A switching regulator converts the power in to the power out so that voltage in * current in. For a regulator that reduces the voltage (switchmode regulators can increase the output voltage, something that linear regulators can't), the input current will be lower than the output current by almost the ratio of the voltages.
The advantage for you is that you can transfer far more of the energy in a battery to the load if you use a switchmode regulator than if you use a linear regulator.
In your case, efficiency really means a lot. It also means that you can use batteries that have more energy for a given size/cost. In your case, a pair of AA cells may be a lot cheaper and have equivalent (or higher) power to a 9V battery. (Clearly in this case you need to use a boost switchmode regulator).