Ideally there should be no difference! Firstly, this depends upon the strata, and secondly upon the drilling technique. For example, if you are in a fine water-bearing sand which is prone to flighting from the Archimedean screw effect of the auger, then potentially there could easily be a difference, and the reason here is, that a larger diameter auger has a shallower flight angle at the auger/soil inter-face, than a smaller diameter auger. The shallower the angle of the flight at the auger/soil inter-face, the greater the propensity for flighting, so potentially (with a larger diameter auger) the flighting could be greater, leading to the loosening of the surrounding ground being greater, and hence the shaft friction lower (with potentially the concrete usage being proportionally higher too).