You may find yourself hunting through all the batteries at the drugstore, trying to find an LR44 to buy instead of a 303/357. All because you want to be ‘faithful’ to MnO2. (By the way, this particular day you won’t find one.)
Functionally, these button cells are essentially interchangeable, but they have different active materials inside them. The LR44 is an “alkaline” battery which has the overall reaction:
3 MnO2 + 2 Zn = Mn3O4 + 2 ZnO
The 303/357 is a silver oxide battery having the overall reaction:
Zn + Ag2O = 2 Ag + ZnO
They both give you a potential of about 1.5 V. Actually, the silver oxide battery voltage is a little higher, and its capacity is a bit bigger. But if you’ve been concentrating on MnO2 for a couple years in your work … you know … your loyalty might kick in.