If, as stated you have the p500 versus the b500, the specs say that you already have shutter speed priority as a manual setting. That along with the zoom are usually sufficient for good bird photography.
The reviews on the p500 and the p900 both mention soft pictures as a weakness.
In terms of comparison, the b500 I use also produces soft pictures and I really like sharpness in a pic prior to editing.
Of course the larger zoom is the big draw, so if that's your main need, the p900 will do. It seems that many of the Nikon superzooms have a very slow focusing time at full zoom. That has also been my experience.