I've never had any wireless carriers other than VZW so I can't speak for Sprint. I've never, ever ever had issues with lost reception or terrible data signals--where I work, pretty much no one else can get reception except those of us with VZW. That being said, if you want special attention or the ability to talk your way out of superfluous charges (e.g. the $30 upgrade fees) VZW isn't great. If you ever have any issues, you'll have a hard time getting things sorted out.
If you have issues with Sprint signal strength where you live/work, you might as well switch carriers.
About the DNA specifically:
-The camera is suitable. Not bad by any means, but by no means an improvement in 2012 cameras. I actually think the GSIII's camera is slightly better, especially for video recording.
-You want a gorgeous screen? The DNA's perfect. Stunning display.
-This might be an issue with my DNA specifically, but if you use it for anything other than texts/calls, it won't last you the whole day. Just wifi web browsing on min screen brightness with 4g/gps/etc disabled, I can't get more than 4 hours' screen time (probably less). The battery rots rapidly even when the device is off or asleep, at least compared to my old phone. Keep an external battery charger handy.
-Depending on your data plan, I wouldn't rely too heavily on cloud storage. If you consume a lot of media and plan on uploading lots of pics/videos, and if 11gb usually isn't enough for you, you might want something with expandable memory. I'm on an ancient plan where 2gb is $30/each phone, so I leave my stuff stored on the device until I have wifi access. Though, despite having most of the apps I'll ever need, and 2gb of music, I still have a decent 7gb of space left.
-If you really want the latest version of Android, you should look into Google devices. Who knows how long the DNA will be on 4.1 (not that I care, JB is great). My Nexus 7 got the 4.2 update as soon as it was released.
Bottom line--if Sprint isn't living up to your expectations you should switch. The DNA is a beautiful device but it has its drawbacks. If you're not in a hurry you might as well wait a few months and see what flagship devices come out in Feb/March.
//if you want the DNA for cheap w/o tax, Target's online mobile store has it for $150. Straight from VZW it's like $250 (in CA tax on phones is based on the full price, idk idk if it's different elsewhere).