The 357 battery is a silver oxide battery, while the LR44 is an alkaline battery. The 357 battery has a longer useful life and provides a more consistent voltage level than the LR44 over time. The 357 battery is also more expensive than the LR44.
The 357 and LR44 batteries use different materials and different chemical reactions to generate electricity. The silver oxide 357 battery is superior in performance to the alkaline LR44. The 357 battery maintains a constant voltage near 1.55 volts until its chemical energy is near depletion, at which point the voltage drops precipitously. The voltage of the LR44 alkaline cell drops continuously over its discharge lifetime.
The 357 has approximately double the useful capacity of the LR44, even though manufacturer's stated capacity ratings in milliamp-hours may appear more equivalent. The voltage of the LR44 can become too low to properly operate a device due to its more rapid rate of voltage reduction, even if additional electrochemical capacity remains.
The 357 battery and the LR44 battery are interchangeable for most applications, but devices requiring a consistent voltage, such as precision calipers and some watches, benefit from the constant voltage performance of the 357. Devices with greater energy demand benefit from the greater useful capacity of the 357.