A simple answer would be that you have an extra parameter which can model an asymmetric peak. For chromatography there is the supposed additional advantage that it models the physics behind it better. At least according to this reference:

http://onlinelibrary.wiley.com/doi/10.1002/cem.1343/epdf

Simple answer is that there is no simple answer, but I will give it a try.

The idea behind the EMG (Exponentially modified Gaussian) method was to deal with the reality that in HPLC and GC, the assumption of a Gaussian peak shape may not be valid. In such cases, IF proper leading and ending points are well defined, then the EMG model is one way of improving accuracy in the measurements. *If the peak is Gaussian, then no improvement should be seen.

However, the real, though not complete solution is to develop high quality chromatography methods which result in clean, Gaussian shaped peaks. These are what the best chromatography integration algorithms are equipped to deal with. Well developed methods with flat, clean baselines should always be the goal. This result simplifies the types of tools needed to generate quality results.

Regarding literature on the EMG model, there are hundreds of well written papers on this topic (many written in the 1970's and 1980's) so please do a simple "Bing" search and you will find more free papers and articles than you can imagine to read. Example: Chromatographia, 1988, Volume 26, Issue 1, pp 285-296.