I'm still using an iPad (1st Generation) so I can't comment on picture-taking apps other than to say that with the consistent improvement to the standard Camera, particularly it's accessibility from the lockscreen, I find it's my goto camera on the iPhone 4S 99% of the time.
In terms of photo editing, the vast majority of my post production, including cropping, adjustments, filters and frames is done in one of two apps:
By far my first choice for cropping, framing and post-production adjustments. The Selective Adjust feature makes this the killer app for photo editing. It allows you to set adjustment points on your image and apply the adjustments only to the defined areas.
Photogene for iPad
Before Snapseed was released I did most of my photo adjustments in Photogene. These days I primarily use it for the Collage feature, but it remains a credible editing app in it's own right.
Photogene 2 is available for the iPhone and features a unique scroll wheel interface.
I have a handful of additional filter apps, but these two (three?) are the must have's.