Any unit on the losing side doesn't apply the difference in Combat Result scores for Break tests so long as its number of ranks is higher than that of all of the enemy units in the close combat – compare the unit's ranks to the enemy unit with the most ranks in the combat. If even one enemy unit has an equal or higher number of ranks, then the unit must test using its modified Ld.
Note that this applies on a unit by unit basis – having one unit with a higher number of ranks does not make all of your units steadfast. Units that have more ranks than all of the enemy units are steadfast; units that do not, are not.