It's the combination of aperture and shutter (a.k.a. "speed") that determines how much light is received by the sensor (like a faucet: how much water you get is controlled by how much you open the faucet (aperture) and how long you keep it open (speed)). But it's not just how much light you receive, so different combinations have their specific uses.
Aperture controls focus blur (a.k.a "depth of field" or DoF), shutter controls motion blur, so it depends which one you want to reduce, or which one you want to take advantage off.
For instance, in an air show, you want to keep some motion blur when shooting propeller planes to avoid freezing the propeller (otherwise it looks like the engine is stopped) so you use speeds around 1/250s. No such problem with jets that in addition are somewhat faster, so you use much higher speeds (1/1000s or more) if there is enough light.
In many other cases (portrait, architecture, macro photography) you want to control DoF, so your main choice is aperture, and speed is whatever is fast enough to keep motion blur in control.
These two are why cameras have "Aperture priority" and "Shutter priority" modes. You set one of the two and the camera adjusts the other for proper exposure.