I have photographed the moon zoomed out to 500mm or so with my Lumix FZ150 when the sky is not very dark and have successfully captured terrific detail in the moon's features. However, when trying to do the same with a dark or black sky, my eye sees the features, but I think the contrast is too much for the camera. I tried using a polarizer, and then a ND filter to no avail. Would I have more success with a full frame sensor camera with many mega pixels, or will all cameras have limitations?
The dark sky around the moon throws off the camera's exposure meter. You need to drastically underexpose the overall photo in order to see the details on just the moon.
The simplest way is to use manual exposure and trial and error. You can also make use of the Looney 11 rule
The basic rule is, '"For astronomical photos of the moon's surface, set aperture to f/11 and shutter speed to the [reciprocal of the] ISO film speed [or ISO setting]." With ISO 100 film / setting in the camera, one sets the aperture to f/11 and the shutter speed to 1/100 or 1/125 second (on some cameras 1/125 second is the available setting nearest to 1/100 second). With ISO 200 film / setting and aperture at f/11, set shutter speed to 1/200 or 1/250. With ISO 400 film / setting and aperture at f/11, set shutter speed to 1/400 or 1/500.
You can also just use (-)exposure compensation to underexpose but you will still need trial and error to get it right.