Sorry, misread. For example,
The relationship between brightness and luminosity is,
brightness = luminosity/ 4 pi r^2
So if one is brighter than the other, say at 5 and other at 6.
We get,
6=luminosity/4 pi r^2
5=luminosity/4 pi r^2
If they had the same radius, then the one with brightness 6 will have a higher luminosity. But however, there might be a difference in size. So it is not necessarily true.