People may use cameras with built-in reflective light meters exclusively, and produce perfectly exposed photos.
They still may not even have a clue about incident light metering.
The difference you noticed, Stradibarius, is due to the brightness of the subject.
It plays no role in incident light metering. But does in reflected light metering.
You will have to correct the reflected light reading for the reflective properties of the subject.
And when you do that, you'll find (or should find anyway) that the two agree, that both lead to the same exposure settings.
You can only correct for the subject brightness by comparing it to that of a standard surface, a surface whose reflective properties are well known: the grey card already mentioned.
As you see, incident metering leads to the desired result quicker. It involves less separate steps, thus less opportunity to make mistakes.
So whenever you can, choose incident light metering.