70-300 vs 55-200 for a Nikon D3200
I own a Nikon 18-55 VR and a v 55-200 (no VR). I love zooming as much as I can, but I have a very limited budget. I am not a professional, so I am learning through experimenting with my camera.
An idea crossed my mind, to sell the 55-200 and buy a 70-300 one instead, either Sigma or Tamron which are both low-budget lenses. Would switching make sense? I mean, I do not know how much zoom is 200m or 300mm, like the compact cameras which appear to have 3x or 10x zoom.
So is the no VR/VC Sigma or Tamron 70-300mm lens any good compared to the Nikon 55-200 ?
We get questions similar to this quite frequently, and it's really kind of hard to answer. See for example this one or this one. Basically, if the answer wasn't "it depends", there wouldn't be so many options.
On how these numbers relate to "3× zoom" or "10× zoom", see How do I convert lens focal length (mm) to x-times optical zoom?
You might also find How can I visualize or simulate the effect of different focal lengths? to be helpful.
I would also highly recommend considering optical image stabilization in your lens selection. It will make a bigger difference than lens quality or maximum focal length in the quality of your images unless you are using a tripod. On a 1.5 crop body, 200mm is the equivalent of 300mm on a full frame, and that is a fairly long zoom. 300 would be the equivalent of 450 which is extremely long (like able to make out people with a fair level of detail almost a mile away if they have sufficient resolution).
As far as a comparison to a 10x zoom, 10x is a useless measure. Without a base focal length, it could be a wide angle lens with almost no range (say 1.5mm to 15mm) and even with a major crop factor, it would still only be like an 8mm to 75mm lens on a 35mm which is wide angle to standard zoom.
The bigger concern I see with your situation is losing the 55-70mm range. That's a fairly key range that is equivalent to the 75 to 105mm range in 35mm lenses. That range is the prime head and shoulders portrait range. Perhaps you don't have a need for that range with what you shoot, but I'd play around a bit with seeing what you'd be losing if you couldn't cover that range.
Overall I think you'd be better served with a 55-200 that has VR though if the only options are either add VR to your current lens or extend your focal length range and still not have VR. It simply has more practical value in resolving a telephoto image. (sharp and less zoom is better than blurry and more zoom.)