Daggah, the two focusing approaches (via live-view and AF) work on different approaches. Live-view focusing takes the image off the sensor and displays it. So a live-view focus is as sharp as you can get. The AF module is separate from the sensor, and is supposed to be at the exact same optical distance as the sensor, but due to manufacturing tolerances and occasional mis-alignments, it sometimes isn't. So the in-camera micro-adjustments (for cameras that support this), or a visit to the service center, serve to bring the AF sensor closer to the same focusing distance as the lens-to-sensor distance. In my own case, I was getting some back-focusing issues that were visible (and annoying) when I was shooting wide open - the actual focus would land a few inches behind the target (which was focused on using the center AF point). I went through the test sequence of shooting an inclined target, and using live -view, my focus point would be exactly where I placed it. When I enabled the AF, my focus point was still the same (camera on a tripod, no physical change) but the resulting plane of sharp focus on the image was slightly behind my chosen point. When I sent in these images to the service center, they immediately agreed that it was a back-focusing issue and asked me to send it in, which I did. As I noted in another post, the resulting focus adjustment placed the AF focus plane much closer to the actual target point (still not perfect, but much better than before).
In terms of testing lenses, there is a strict protocol that works - the target needs to be exactly parallel to the plane of the sensor, your lens axis needs to be exactly perpendicular to the plane, the camera must be on a sturdy tripod/head, with techniques used to prevent camera movement (mirror lockup, remote shutter release), and the light must be steady and consistent and high enough that you can shoot at f/32 without using a slow shutter. Focusing is done by the live-view method with 5x or 10x magnification (if available). The target itself needs to be very high in contrast with barely-resolvable fine detail (there are a number of downloadable targets available). Of course, any filters need to be off. Using this approach, despite my slightly wonky AF, I was able to work through my lenses and determine their sweet spot (and amount of resolvable detail at center and edges) to my satisfaction.
Another real-world characteristic that is present in lenses is contrast. This seems to be related to the light entered the lens off the optical path and making its way to the sensor. The best lenses appear to manage this extraneous light very well, the cheap lenes less so. So another test I did with my lenses is to put a bright LED flashlight shining at the lens (but out of the visible frame) to see if and how the resulting contrast was affected. Again, eye-opening. Some lenses really need their lens hoods to give a contrasty image. Others are less prone to this. But you need to test it to see the results yourself.