One option is a cloud service. Dropbox lets you automatically upload pics from your smartphone which can be then accessed from your new phone. Or Google+ can sync your photos to your Google+ account to a private album. The downside with any cloud service though is time, it takes lots of time to upload photos, but it at least happens automatically. Downside number two is data. It takes lots of data to upload photos. You can set most services (including the above) to only sync over WiFi, but that may be inconvenient in some cases. But a cloud service will take up less physical space on your new phone.
Or you can do it the old school way by hooking up to a PC and moving all the media files from your old phone to your desktop and then hook up your new phone and transfer the files. The files will be on your SD card (showing up as a secondary mount with your phone's internal storage being the primary; so it'll look like two usb drives on your desktop basically), and then pull the photos from the "DCIM" folder on the SD card (beware there is a DCIM media folder in your internal storage as well). You can either grab select photos or just copy the whole folder to your liking. Then once you've grabbed what you want and copied to your desktop you can drag and drop, or paste, into the DCIM folder on your Droid DNA. And there you go!
The second option requires a PC of course, and it takes some digging, but the transfer will take minutes instead of hours and it is fairly easy especially if you're comfortable with using files on your computer and on your phone.
If you're not sure what's on your SD card when looking on your PC you can always download a file manager app from the Play store and you can find the DCIM folder right on your phone. I'd recommend having a folder browsing app anyway, there are many good ones, but I'm using Andro Zip now and I like it a lot.