I came from an iPhone 5, which most would say has a superior battery and camera, so I feel like I can give an honest opinion.
I've gone pretty much back and forth from Android to iOS over the years. I just started using my Nexus 5.
1) Camera - I can't speak *too* much about the camera yet, because I've only just started using the phone in the last few weeks and haven't had any trips or anything where I'd take a lot of pictures. Overall, in my limited use, the camera is not as good as the iPhone 5, but is certainly good.
The recent update supposedly fixed a lot of the initial complaints about it. I never used it prior to the update, so I can't comment on it. If you look on r/nexus5 and other places, people show some really beautiful pictures with the camera. I think it is possible for it to be as good as the iPhone if you learn the different settings, etc.
I think unless you are a huge photo-holic, the Nexus 5 is more than adequate. And if you are that picky about pictures, most would tell you to get a DSLR anyway.
2) Battery - This was my number one concern coming from an iPhone 5. I absolutely loved the battery life on the iPhone. It truly is unvrivaled.
That being said, I've been very impressed with the battery life on the N5. I've been charging it in the evenings on my home computer, then unplugging it all night, and using it on and off all day at work, and coming home to at least 30% or more battery remaining. I seem to get at least 24 hours of up time with 4 or so hours of screen time.
I haven't been monitoring it thoroughly, so my evidence is anecdotal, but my bottom line is that it was my number one concern coming from an iPhone and it is no longer a concern. Very impressive battery. Check out the Anandtech charts:
http://www.anandtech.com/show/7517/google-nexus-5-review/3
Hope this helps!