This is a quite common question and the answer is more than easy. Every time someone asks you if you need to print your project litho or digital ask yourself how many copies you need.
Usually Digital Printing is more suitable for shorter runs and Litho for longer runs. The difference in terms of printers is not something you need to know right now but we could explain it in this way, a digital printer is just like your printer in the office but better in quality, for the litho look what JR Art Guys have put together and check how old fashion and beautiful are the machines for this kind of print.
But don’t get confused because if you need to print 600 business cards for example the digital printing could be a good for you in terms of timing. Usually the turnaround for litho prints is longer than digital.
Another thing you have to take into account when you print Litho is that you can choose between more kind of paper and thickness (Digital machines will run on stock weights between 70 gsm and 300/350 gsm), in some cases you could find a better quality on litho prints, and you can use different kind of effects and special inks.