It's not always true that digital distribution of media will have lower carbon emissions than distribution by physical means, at least when file sizes are large.
That's the conclusion of a study published in Yale's Journal of Industrial Ecology that looked at the carbon footprint of games for consoles such as PlayStation®3. Researchers found that Blu-ray Discs delivered via retail stores caused lower greenhouse gas emissions than game files downloaded over broadband Internet. For their analysis, the investigators estimated total carbon equivalent emissions for an 8.8-gigabyte game because data for 2010 indicated that to be the average game size. The bulk of emissions resulted from game play, followed by production and distribution.
The Internet will become more efficient with time, but game files sizes are likely to continue to increase, making predictions about the relationship between online services and climate change a matter for further research.