Is Azure's B-2 app service plan better than a S-1 for production environments?
The B-series has this name from burstable adjective.

It means that you do not have 100% of the cores for 100% of the time (see Introducing B-Series, our new burstable VM size).
For example B-2 you have guaranteed only 40% out of a potential 200%.

The suggestion to pick a different serie for production workload, is to guarantee the CPU available.