I like binders, and have several for various purposes. I plan to set up a few more. I prefer the thinner ones (1 1/2 inches or narrower), as I find that I rarely need a wide one for a particular subject, and the larger ones are harder to handle.
On the other hand, I still keep a lot of info in my filing cabinet, because the total space required is less. The narrowest binder is at least 1/2 inch, whereas most files are narrower than that. Some files have maybe 1/8 inch of papers in them. So part of what determines if I use a binder or not is what I need to store, or how many "subdivisions" I need. I set up a binder for Toastmasters and for my computer because it was easier to organize and find material than to just have it in a folder. I tend to have in binders things I refer to more often, and in folders items that are more for occasional reference.
I highly recommend color-coding binders to make it easier to find what you are looking for - unless you prefer a uniform look and have some other way (numbers?) of quickly telling them apart.