Regina’s lack of emotion could be because she’s emotionally numb inside after Robin’s death. It came as such a shock that she can’t process what’s happened and she’s gearing up to go off the deep end.
Emma’s tearful reaction could be because she’s feeling guilty. If she’d never dragged everyone to the underworld, Hades wouldn’t have got to Storybrooke and Robin wouldn’t be dead. Emma would feel that Robin’s death is her fault.