I have taken some very beautiful bird pictures with a 55-250mm lens on a crop sensor entry-level Canon DSLR. It's 400mm equivalent (35mm). On your Nikon, the 300mm is 450mm equivalent (35mm), i.e. longer.
I would say a much longer lens would be significantly harder to aim. But, since you have a crop sensor camera, a lens zooming to 400mm, 500mm or even 600mm would be an option. These are 600mm, 750mm and 900mm equivalent (35mm), i.e. very long. Unfortunately, they cost more than a 70-300, and the weight is something totally different than the weight of a 70-300. They also are physically longer.
On the other hand, I don't always get many keepers with a 400mm equivalent (35mm) lens. I think these factors affect the number of keepers:
- Whether I can get close enough to the bird
- Whether I have a good background
- Whether I can photograph the bird in an interesting state, such as starting or stopping flight
...but perhaps the largest factor is just the amount of luck.
I have given up trying to photograph small birds in flight because they fly so quickly and on such an erratic path that it's almost impossible to get keepers.
Remember to use continuous focus, and set the shutter speed to 1/1000 to get good pictures that are in focus and don't have motion blur, if photographing during the daylight. In anything other than daylight, things become significantly harder.