Tamron 70-200 F2.8, bit expensive but very good.
Make sure you need the 300mm reach as it is not that much more Tele than a 200. You will defo need either plenty of light or a tripod for that much reach if your lens does not have VR (probably you will need VR even with plenty of light if you dont have steady hands).
The 70-300 VR from Nikon is very good also, has VR and the extra reach you are after. It is twice as expensive as the 55-200 though.
If you have to be restricted to the two you listed then I’d go for the 55-200 and if I need a bit extra reach I will just crop.
MOLGRIP: Yes, pretty much all new Nikon lenses and most Nikon mount third party lenses have motors in the lens. Lower end Nikon bodies (D40(x),D60,D3000,D5000,D3100) do not have AF motors so if your lens does not have one then you have to manual focus.