You have to be careful here, as I understand it, Live View on Nikon is What you see, is what you get. So in low light you may have to open up the lens a good bit to focus, and get around the nonbuffered noise that tends to show up. So example in low light I will open up the 24mm all the way or to at least 1.8 as it makes a huge difference in ability to focus, but I know that for the shot, I need to be at F6.3, so here you may get some focus shifting if the lens has the problem. If you try the other angle, staying at F6.3 and then dialing down the shutter speed to where you get enough light to foucs, it's again hard as the live view is reacting to the slower shutter speeds. At least this is what I have found in practice. In normal light the Nikon solution seems better to me now as I like the what you see is what you get.
Here is where Canon figured out a way to buffer out the noise in the lower light focusing, i.e. late at night, early morning etc. You can have exposure problems here too if you don't look at the metering display as the live view shows most times even exposure even if your current settings are not. But again it's a bit easier to me for the night work, and lower light work.
I really never realized all the benefits to liveview for focus until I started working with Nikon where it seems to be very critical at times.
Paul