What is the best and most reliable airline to use to fly from Nice FR to Rome IT?
Depending when you plan to fly, the options are variable, by day of the week and available airlines.
For a one hr flight it really wouldn't matter to me.
Check Skyscanner and see what's available.
Just be sure whatever you choose to follow the luggage limits precisely — often you may need to purchase a special ticket to be able to bring a second carry-on on board, for example. And to be able to check a bag if you need to.
There is no big difference in reliability across airlines; however, low-cost airlines such as Ryanair, Vueling, Easyjet, Volotea have very strict luggage policies that you MUST follow - or it will be expensive. Headline prices typically do not include cabin luggage - only an underseat personal item.
We flew Florence to Paris and chose Air France due to the "cheap" airlines limiting our luggage weight and flying into an airport that would have cost more in taxi fare to get us into central Paris. The cost was only like $70 each one way.
We used Easyjet. was fine