When Aristotle formulated his dialectic system he thought he was modelling human reason as we use it in practice, and I believe he was right. We do reason our way to conclusions just as he proposed.
But few people use his system as he specified and the result is that his 'laws of thought' and dialectic process have been doubted as a way of arriving at truths. If used properly it is reliable, and I see no evidence that we use any other logic when reasoning.
In philosophy this problem of the misuse of Aristotle's logic is acute, for it leads people to false conclusions and seems to force them to invent paraconsistent logics and other exotic systems.
I would recommend C. W. A. Whittaker's book, Aristotle's De Interpretatione
which explains how to use the dialectic properly.
So my answer would be that Aristotle's system is the one we usually use, or intend to use and should use, but that we don't always use it properly, especially in philosophy. Of course, it depends on having appropriate starting terms. Often his system is inapplicable because we are not able to define a contradiction clearly for logical purposes as in the case of bald men or a pile of sand, which are ambiguous objects requiring definitions and judgements that go beyond logic.