HSI and MSI - Applications of two Internal RC OSC in Microcontroller
HSI is way more accurate, while being less flexible.

Looking at the highlighted values in the datasheet, MSI frequency becomes extremely unreliable at the lower ends of the temperature and the supply voltage range, while HSI would barely notice VDD dropping from 3.6V to 1.8V.

Therefore it is quite surprising that you were having problems with HSI as a clock source. Adding a bit in the middle would mean about 20% clock drift. That's a magnitude worse than the theoretical worst case accuracy of the HSI. There must be some other issue still lurking.

It is also worth noting that HSI16 can run in the STOP modes, but MSI can't.