How to think while comparing approaches
Not knowing the details of your project, I'll offer some general suggestions.
In a sense, it seems to me you're asking two problems:one question is how to read papers, the other question is how to compare methodologies.

As far as comparing methodologies, the key concept in my mind is that of a "metric" or some means of judging/ranking methods. In CS, for example there are many such metrics: computational complexity, run time, stability, theoretical results regarding convergence, etc. Metrics often are often context dependent, meaning that different classes of users may have different ways to rate/rank a method. An algorithm may give an exact answer, which to a theoretician may be great, but if the algorithm can't function in real-time, another use may prefer another method that gives an approximate answer but quickly. So know who is going to use the methodology often helps you understand what metrics are really significant. So two thoughts to keep in mind are the methods you learned in class for judging how good an algorithm was and also who is going to use the algorithm (what are their concerns/needs and which methods best addresses 
them).
A suggestion in this regard that will also help you with your paper reading is to look at what the authors of each paper say are the advantages of their method. In the introduction every author will give a reason why their method is "better" than the other (existing) methods.