Both digital and litho offset printing have their advantages and disadvantages. Like all manufacturing processes it depends on the job in hand, which way it is produced.
At its most basic, digital printing is generally a toner based printing system that takes very little time to set up once the artwork has been created. However each individual copy has a relatively high fixed cost. On the other hand, a traditional litho offset printing press uses oil based inks ( generally ) and take alot more time to set up with expensive printing plates. However once it is running the individual copies are very cheap to produce. This means that if you are producing a small print run digital printing with its low set up cost is better value than litho offset printing. However if it is a medium to long run litho offset printing is by far the best value because its low copy cost outways the set up.
Another factor to bear in mind is that litho offset printing generally speaking, still produce far better quality results than toner based digital systems. Furthermore a traditional press can print on very nearly any paper or card, where as with digital, you are limited to a narrow range of materials specifically designed to cope with toner based systems.
It is my personal belief that the current toner based digital printing systems are a technological dead end and the the future lies in hybrid inkjet machines. In other words a digital inkjet delivery mechanism in a traditional mechanical paper handling and delivery system ( currently used on litho offset presses ). This would combine the subtlety of liquid ink for quality, the robustness and accuracy of litho offset paper handling and a reduced set up cost.
Modern Print offers both a digital and litho offset printing service.