@Finite That's not quite right. There are two ways to look at apparent brightness: surface brightness of an object or the overall brightness of an image (whether it's at the camera sensor or on your retina).
As far as the visually observed surface brightness of an object goes, for a given eyepiece a faster telescope will yield brighter views. Aperture does not matter: only f-ratio and the eyepiece focal length matter. Actually it's a combination of these that determines visual (surface) brightness: the exit pupil diameter = eyepiece focal length divided by f-number of scope = telescope aperture divided by magnification.
However, for the same exit pupil, a larger aperture telescope will yield higher magnification. Hence you will be able to see deeper and (if seeing allows) in more detail. If you are looking at an extended object, like a large gaseous nebula (think Orion or Carina) then it will take up more of your field of view at higher magnifications, so the image overall will appear brighter. But the apparent surface brightness of the nebula itself will still only depend on the exit pupil. It's perhaps a little counter-intuitive at first, till you think about it.
Or you can think of the Moon. Its surface will appear just as bright through 10x50 binoculars as through a 10" telescope (250mm aperture) at 50x magnification. But because the Moon will be 5x bigger in the latter case, the overall perceived brightness will be greater: you have 25x more light entering your eye from that much larger looking Moon. Note that the exit pupil in both these cases is 5mm. (Hope this make sense.
)
Useful exit pupils fall in the range of 0.5mm to 7mm (from highest to lowest magnification and dimmest to brightest views). But in practice the range from 1mm to 5mm is more useful. Much below 1mm one tends to see no more detail (the image is just gets bigger, but also dimmer and blurrier). Above 5mm, your start running into the limitations of your own eye: how wide your pupil can open. If you're in your late teens to early 20s, nature gives you 7mm (or perhaps even a bit more). As you age this drops. I think for someone in their 40s, 5mm is average.