I'm going to go out on a limb here and say that "the perfect fit" sounds odd whatever the context. I think you want "a perfect fit". Your new suit is a perfect fit.
I agree that this is what the words appear to mean, but I think the two expressions are frequently used with the same meaning today - it fits me perfectly.
By the way, if it fits me, it is the right size; if it suits me, it looks right on me, it goes with my physical appearance.
I'm going to go out on a limb here and say that "the perfect fit" sounds odd whatever the context. I think you want "a perfect fit". Your new suit is a perfect fit.