I have the DA 55-300 and the DA*300, and have rented the Sigma 50-500. You can get good results with any of them, with the right conditions and technique. The 55-300 does well as long as you have good light. The Sigma has the reach, and the DA*300 has lower light ability, and I think stnger image quality. Technique is steadiness, patience, scouting, LUCK, and knowing your equipment. The focus on the 55-300 is slow and noisy, learn to manually focus with quick shift and then hit the AF, especially through trees. I like to use burst (Continuous High Shooting) too. Here's
thread on Lenses for Birding that a lot of top bird shooters replied to.
If you look at the EXIF of these sample you'll see with the 55-300 I was lucky to get sharp shots at those low shutter speeds, my copy is optimal at f8. I had pretty good light on that shot with the Sigma, and the DA*300 can be shot at f4 all day, just less depth of field. These are all handheld and all warblers, which are tiny birds no more that 4 inches long.
55-300:
Sigma 50-500:
DA*300: