I've recently been using Enlight to take pictures and edit them on the iPhone 5s. I became aware of it just a few days ago after seeing it highlighted in the App Store and decided to give it a shot. I've tried quite a few photography apps (I'm willing to bet more than $100 worth of them in the last year or so) over the years, and this one just seems to hit all the high notes for me - it has a clean interface that hides some fairly advanced editing tools, including and interesting swipe control for applying effects where you can dial in the effect to exactly the level you want by dragging your finger left (less) or right (more). These editing tools can be as simple as one tap, or if you desire can be fiddled with and customized to create your own looks. I really enjoy my custom presets in Lightroom on my iMac, so this feature fits how I think about editing photos.
The kids (especially Joe) are rarely still enough for me to get good pics of them anyway without using the bigger, faster cameras so this interface being fairly simple (not the full on bells and whistles of some of the other more camera-focused apps (like Manual) isn't so much of an issue for me. Maybe when I upgrade to the 6 or 6+, I'll revisit those apps.
If you are looking for something a little less-fiddly, I also like MagiCam for taking pictures fast and applying one of ~8 premade presets. It does a really nice job right after you take the picture - lots of those pictures (particularly outdoor ones) need no more editing other than a crop after the app applies the selected preset.
When using the big cameras (like when on vacation when I don't have my iMac at hand every night), I really like ShutterSnitch for moving pictures to the iPad (you never have too many backups!). These are usually then edited in Pixelmator or Handy Photo on the iPad. Pixelmator is brilliant - I've really only scratched the surface of the iPad version, but the Mac version has replaced Photoshop for me. I just couldn't see signing up for the suscription service for the Creative Suite, and would honestly have thought had about upgrading Lightroom if it had been included in that. Handy Photo is also very cool and was one of the first apps I'm aware of to implement clone stamps for advanced editing on the iOS platform. Their Magic Crop feature is bonkers too. Both of those are highly recommended.
I'll update this post as things change (and as I remember to do so), but this is a pretty good look at what I'm using these days.