PB,
Aircraft on an MLS approach use the MLS 'localiser', technically called the 'azimuth', not the ILS localiser.
The benefits are all realised in low visibility (600m vis); assuming a pair of landing aircraft with the follower on an MLS approach, the lead aircraft has to be 82m from the centreline of the runway to enable a landing clearance to be given to the follower. Compare this with 137m if the follower is on an ILS approach (150-192m if the lead is an A380).
However, it is true to say that the new wide apature array ILS localiser systems coming into use now have similar benefits.