I do not own the 55-300 but I do own the DA*300. Simply put, it's a marvelous lens. I don't do birding myself but do love zoos; sometimes the lens has just a bit too much reach for that, but when that's not an issue, the lens's quality is impeccable.
Unfortunately, I don't have any photos of animals I can upload at the moment, but here's a bunch of photos from a high school hockey game I attended a few days ago. It was my first time to shoot sports ever. (And boy, it's hard to pick a bigger challenge than hockey!) These were shot wide-open at f/4 at 1/400 sec with ISO1600 on a K-5 IIs. All were handheld.
Please excuse the less than perfect framing. In addition to being my first time shooting such a scene, the lens had a little bit too much length for the small arena. I tried to back up a little, but that didn't help much (poor angle). 250mm would have been perfect, but all I have is 70-200 and 300. These are JPEGs straight from the camera.
You can get to a full-sized version by clicking on the image; feel free to pixel peep away.