FF = Better low light performance?
Do you have a weird meaning for brighter in mind?
Or do you mean brighter like in" I took two shots of this same subject using the exact same camera and lens and light and set one at f5.6 and once at f8, and the f5.6 picture was brighter"?
That kind of "brighter?"
If so, the sanswer to your question is no.
One full frame shot and one crop shot, both at same ISO, both of same subject, camera moved back with crop to show the exact same amount of subject as the full frame camera, both at same aperture, both at same shutter speed, using a EF lens so that it will work on the full frame and on the crop body, will be identically bright.
Willthis help your thinking? Let's see. Many professional photographers sometime use external handheld light mters to determine what exposure settings to use.
The meter is set to the ISO of the camera (film or digital sensor), and pressing a button gives you an aperture and shutter speed. There is no setting on the meter toalter the setting ifit is usedfor a so-called crop sensor, a so called full frame, a35mm camera (same as fullframe) or a 645 or 6x6 or 6x7 or 6x8 or 6x9 or 4x5 or 5x7 or 8x10 camera.
To get really nit-picky, sometimes, on larger format cameras, the effectiveaperture changes when the lens focusses closer, but that does not matter in your case.