This article from this thread highlights another benefit of continuous sampling. In continuous sampling the conversions are triggered by a h/w clock, so regardless of what the f/w is doing that sampling is going to occur as regular as clockwork. If f/w is in charge of kicking off each conversion, then you introduce jitter into the sampling.
It’s important to note, that if you want low noise and good frequency resolution from your ADC, you will need to sample at a very consistent rate. To do this, you can use first conversion mode, free running mode, or an interrupt that is a multiple of your ADC clock. All other modes will have 1/2 ADC clock jitter. This will cause your samples to not line-up in time, and slowly wander back and forth, effectively causing a frequency modulation of your signal.