I have the exact same problem. The large image twitter card sometimes displays as a regular summary card in search results on my profile page and on mobile devices in the twitter app. With regards to the app, it seems to behave differently for different users/devices, ie the same tweet on two different Samsung phones used different twitter cards.
The difference between search and feed doesn’t bother me so much, but I’d like the tweets to look the same on mobile and desktop.
Tweet with correct card: https://twitter.com/digestmag/status/346198006959312896
Embed:
Food critics - should they be heard but not seen? Critics, anonymous: http://t.co/11ScB3iyAs
— Digest Magazine (@digestmag) June 16, 2013