The principal for the case study is about the sample N=1. For example, in Health Science, if you find some specific illness in a country or place that never appears before, a case study about it can be very useful for literature also for possible future treatments of this hypothetical illness.
In the other hand, a full research paper required most data and sample of course, but the more sample you can report the more your statistical impact may you have (in theory).
If you answer is in the way about the "difficult" or the "advantage" between this two forms of research report, well in my opinion, both are specific and valuable. If you want to know the best form for you report, you must consider the condition of your sample or study indeed.
For more information, i left you 2 articles and i hope this be useful for you.
I think you would find the following book of readings helpful: Charles S. Ragin and Howard S. Becker (eds.) (1992). What is a Case?: Exploring the Foundations of Social Inquiry. Cambridge University Press. ISBN 0-521-42188-8. The introduction to the volume was written by Charles Ragin. It is entitled "Introduction: Cases of "What is a case?" This seems particularly pertinent (pp. 1-17). Good luck, Bruce
All of the answers here are very good. It's also important to note that an N=1 can mean either "one person" or "one unit". So if your unit of analysis is universities, you could have a case study on one university even if you interviewed or collected survey data from hundreds of people at that university.