Looking to upgrade18-55 lens to a better Zoom on far away subjects (wildlife)?

Presently i'm having Nikon D3200, 70-300mm or 55-200mm

Definitely the 70-300 I had one on a cannon and loved it.

If I had to do it again, I would get the 70-300. I have a 55-200 and it's often not enough. You can NEVER have too much zoom.

I have had both lenses and the 70-300 is much better. It isn't only the extra length. You can get that with the 55-300. The 70-300 is much faster to autofocus and far superior for image quality to both the 55-200 and the newer 55-300 lenses. The vibration reduction (VR) on the 70-300 can also be set to active mode, which is usable from a moving vehicle!