These are not competing products, they are two different operations, and knowing which one your problem needs saves you both money and — more importantly on mature skin — product on your face.
A concealer covers. It is opaque pigment matched to your skin tone, and it works by hiding what is underneath. To hide a strong color difference it needs to be dense enough to block it, which means material, and material is what creases.
A corrector cancels. It is a thin film of the opposite color, and it works optically — reducing how much of the unwanted color reaches your eye. It is not opaque and it is not meant to be. A corrector on its own usually looks slightly strange; its job is to change what the next layer has to deal with.
Put together, the economics are the point. A blue-purple under-eye circle covered by concealer alone needs a lot of concealer, applied to the thinnest skin on your face. The same circle with a trace of peach correction underneath needs a thin layer of concealer, because the blue is already gone and the concealer only has to match tone. Correcting is how you use less concealer, and on mature skin using less is almost always the goal.
When correction is not the answer: a mark that is the same hue as your skin and simply darker — most age spots fall here — does not have a color to cancel. There is nothing for a corrector to do, and a matched concealer pressed precisely is the whole technique. Correction also does nothing for texture: on a crease or crepey skin it is one more layer working against you.
