Wheaten flour has a much stronger flavour. It requires cooking to help remove the rawness that will otherwise ruin a sauce. This cooking means it's not necessarily suited to many sauces or as a general purpose thickener. It also makes it more difficult to add more at the end if you need more thickening.
Flour also has bigger particles, which can cause an unpleasant texture, and contains gluten and protein. It turns sauces opaque (and white) which means it's not ideal for many thickening uses.
Cornflour (what cornstarch is called in Australia), has little to no flavour. It is mostly carbohydrates with practically no protein. It doesn't require any pre-cooking, though it does need to be heated to thicken, and makes translucent sauces (you can kinda see through it) . This means you can add it to many more sauces or other foods. For example, I will add a couple of spoonfuls (dissolved in just enough water) to a stir fry to thicken the sauce so that it sticks to the food better--the time it takes to finish cooking the meat is generally enough to thicken the sauce.
A third option is to use arrowroot, which is the starch from the roots of a variety of plants. It's almost pure starch, which means it has basically no flavour, thickens at a lower temperature than either wheaten or corn flours, and unlike the others makes transparent gels (it doesn't add a white colour to the sauce). This makes ideal for things like clear sauces or soups.