I recently went from a 2-wheel rollaboard to a BR Baseline Domestic Carry-On Spinner, and while it's a great case, I'm not convinced four wheels is clearly better or worse than two. Here are my observations.

-4 wheels takes the weight off your arms and keeps it on the ground
-4 wheels is easier to roll on smooth ground, but harder to roll on anything textured, e.g. carpet, cobblestones, and those nubby metal yellow plates at the end of many sidewalks. In other words, it makes easy terrain easier, and harder terrain harder.
-4 wheels may seem to have more vulnerable moving parts than 2 wheels, but may be treated less violently by baggage handlers. I read an article from one who said that they can simply push spinners across long corridors rather than throw them.
-4 wheels is much easier to push along an airplane's narrow aisles, as it can roll sideways. It can also maneuver around narrow duty-free shop aisles more easily.
-4 wheels is noisier than 2 wheels.
-4 wheels has less capacity as the case starts higher off the ground
-4 wheels can roll away from you on a slanted driveway