I have very little background in SQL (one pet project with PostgreSQL that demonstrated only basic queries up to joins) and no experience at all with NoSQL. I understand that there are many DB architectures that get labeled NoSQL, I'm primarily looking for document-based SQL alternatives like MongoDB, which APPARENTLY are better suited for quick takeoff when you are building a prototype fast and are the most general purpose among other NoSQL tools.
I'm willing to do a research by making an identical application twice - with these two DB paradigms under the hood, and I need help to find a good idea that would help me highlight the differences. I've spent several hours looking for differences on the internet, but all the articles I found seem to just scratch the surface and explain HOW TO USE either SQL or NoSQL instead of when NOT to use each on explicit usecases.
I'm tired of reading the same material all over again and want to get some hands on experience, but I'm very afraid that everything I'll come up with would just as well work with both paradigms, and I will be just unable to understand any difference after I've written the example, because I'll have no trouble implementing. I need some ideas what I can do with each of these but not with its opponent. Could you point me in some better direction than I am heading now? :)