Extracts would be more beneficial for analyzing historical prices where we won't be making use of any real time data being streamed. Same is the case for enormous datasets having billions of rows (extracts will be more efficient in analyzing subsets of such large data).
As for live stock prices, flight updates, real time updates from production or mission critical systems - having a live connection is the most logical choice, since we need access to the most fresh and recent data possible at all times!