I'm pretty sure wild shape works the same way regardless of your starting size. Small-sized druids (like Halflings) don't get "smaller wild shape", so Large-sized druids shouldn't get "larger wild shape".
"Races of the Wild" has racial substitution levels for a halfling druid which give 'undersized wild shape'. This reduces the halfling druid's wild shape sizes by 1. So the halfling druid to Small or Tiny animals at 5th level, Tiny-Medium at 8th, Diminutive-Medium at 11th, and Diminutive-Large at 15th.
I thought I had read something similar for large creatures. I can apply the same idead, 'oversized wild shape' for this half-ogre druid and just increase all of his wild shapes by one size category, but I thought I'd read something 'official' somewhere. Maybe it was in Dragon (or Dungeon) magazine. Or maybe not.