Between-subjects allows us to compare two or more groups that are given two different treatments. Within-subjects allows us to observe a group of participants over a course of time during a process. Using the between-subjects allows us to collect data at a faster rate and thus avoid our participants to become bored or lose interest in participation due to becoming exhausted of having to repeat the experiment more than once. Although within-subjects is a risk for losing participants over exhaustion, it allows us to test the same participants so we avoid other factors interfering with the results. For example, if I want to know if a group of students will test better if they listened to music prior to testing but they all differ in IQs or I do not have this background information to begin with, I can choose to test the same people over some time.
Small or large N designs refers to the sample size, or number of participants that will be participating in a study. Small N designs have fewer participants and large n designs have a larger number of participants. Overall, it is always good to have more participants, but there are cases where a small n design is more appropriate. Large N designs are best when we are able to have a large number of subjects participating. This will allow our study to be more generalized because our sample size is larger.