Done some quick tests with a 800mm mirror lens and shooting at a target around some 5 metre away and come to the following conclusion.
No matter what shooting style, live view gave a slight edge of sharpness in my test...
1 ) Photo
2 ) Photo using live view
3 ) 2 second delay
4 ) 2 second delay with live view
5 ) Remote control photo taken
6 ) Remote control photo using live view
7 ) 10 second delay
8 ) 10 second delay with live view
9 ) Mirror lock up (Canon) 2 shutter presses
10 ) Mirror lock up (Canon) live view
11 ) MLU - 1 second delay
12 ) MLU with live view - 1 second delay
The 2, 4, 6, 8 are all sharper than their non live view counterparts.
I perceive the differences between 9 - 10, and 11-12 as somewhat smaller than the differences between other counterparts, this despite contact with the camera in order to activate the functions.
I got the impression that the remote shooting with live view gave the sharpest result, followed by a 2 second delay, and the mirror lock up and all the other live view photos. It's harder to tell which of the ordinary photos that was sharper but I perceived 1 and 9, 11 as quite similar and probably amongst the sharpest ones, most likely due there's not much difference from pressing the shutter one time, or two times (as long as there's long enough pause between the presses).