It depends on your data and on the library or functions that you're using to analyze your data. Ultimately, in many situations, you can use either. Vectors are easier to work with, but lists are more versatile.
The main difference between vectors and lists in R has to do with the data types of the elements of the data structure you need to use. Vectors require the elements to all be of the same data type, whereas lists can have elements of different data types. In other words, a vector must contain just numeric values, or just factors, etc. Lists can have numeric data in element A, factors in element B, characters in element C, a matrix in element D, and so on.
Statistical and data science functions in R typically output many different quantities that are returned in the form of a list. Here's some sample code I wrote that demonstrates the use of lists.