I have shot a lot of birds over the past few years, started with used Tamrons and Sigmas, then the DA55-300, and now the DA*300. I have also rented a Sigma 50-500 for birding. I have gotten many good photos with the 55-300, but there are limitations and technique involved. It does need to be stopped down a bit and it shines if the light is decent. The screw drive autofocus sound will flush birds in an instant, you can defeat that by quick shifting first to get close to focus manually and then hit the autofocus, eliminating most of the noise. You can only do that with the DA version, not the DA L since it does not have quickshift. I think it is much more effective to shoot birds freehand than with a tripod. That of course depends on the type of birds you are shooting and the location. A tripod is great for a nest or someplace you know the bird is going to be, you'll definitely get better shots when you get them. The birds I usually shoot are small and move a lot, and are pretty impossible to track with a tripod, at least for me. With 300mm you will crop a lot, I did find I prefer the DA*300 over the Sigma 50-500, seems to me the IQ and speed negated the extra 200mm of the Sigma. I did not have a problem shooting handheld with either, and that is carrying them as long as dawn to dusk.
Knowing the habits and habitat of the birds is key. Migration time is the best to catch birds. There are certain paths they take at certain time of the year and they are usually interested in feeding because they are replenishing energy spent from long flights. The past few years I always go to Magee Marsh, Ohio for a few days in May for the Warbler Migration. There are a lot of warblers and other migratory birds that gather near the Lake Erie Shores to feed and rest before flying across Lake Erie. Thousands of people come to the area to watch them and the birds seem to get somewhat used to people there. Opportunities like that are golden. Birds in urban areas are much easier to approach that those in rural areas, they do get used to people. Try to get near a duck in a wildlife preserve and they will fly, but they will come to you in the city park, it's the same with mammals like squirrels and chipmunks too.