If the case study has more than one participant, you may be able to engage in some quantitative statistical analysis of the data. Parametric statistics are not appropriate for this type of research because of the small number of participants (n) and the fact that the participants are rarely chosen randomly, both key assumptions of parametric statistics. Instead, some nonparametric tests may be able to help such as the median test, sign test, and perhaps chi square.
For both a case study and a low n study you are likely to rely heavily on qualitative analysis of the data. It is important to gather qualitative data from a variety of sources in both types of studies such as interviews, participant observation, artifacts (such as tests), field notes, and perhaps audio or video recordings. When analyzing the data, you need these different sources to triangulate your findings. This involves confirming a finding based on one source of data by finding similar results in other data sources. Triangulation of the results is key to establishing validity in qualitative research.
A possible similarity, depending on how the low n study is constructed, is that the participants for the studies may be chosen before the study begins. For example, a case study sets out to examine a particular case, however that case may be defined, and the case will likely come with a certain, invariable group of participants. A low n study may have the same constraints. The participants in the low n study may be volunteers for the study. In this sense they do not represent a predefined case, but rather a particular group of volunteers. In either situation the participants are not selected randomly.
Depending on your field of study, you may encounter resistance to both a case study and a study with a low n, as many people still have some bias against qualitative research. It is important, therefore, to make a concrete case for your research addressing issues such as validity and reliability. Citing prior studies in this area that used a similar methodology and citing research attesting to the efficacy of qualitative research with a low number of participants (or even a single participant) can help you make your case to others.