The camera may be using different focusing points when in "normal" mode and in live-view. In many cameras, the metering is associated with the focusing points used. If your camera is set up this way, you will have differences in the two readings.
When trying to figure out why things are different, it helps to eliminate as many variables as possible. That usually means camera on a tripod (as gsgary mentioned), turning off all the auto functions, and varying ONLY the item you are investigating. So in this case, I'd put the camera on a tripod, select a specific AF point, and try to shoot the sequence: manual mode exposure (you set both the aperture and shutter speed, by zeroing the meter) through the viewfinder, Aperture-priority exposure (set the same aperture you used for the manual shot) using the viewfinder, then repeat the exact same sequence using live view. If this set gives you the exact same exposure each time, then you know that the camera does at least meter consistently. Once you have this baseline, you can change something (say, let the camera pick the AF point), and repeat the exercise. By doing this type of testing, you'll learn how the camera behaves (always a good thing), and you'll know what the different settings do.