I'm gonna take a wild stab at this and say, as you're in the D3100 forum, you have that body.
What is the best lens to purchase. AFS 1.4-5.6G ED DX VR or AFS f/4- 5.6G IF-ED DX VR
I think you've confused yourself with those lenses.
There is no f/1.4-5.6 55-200m lens in any shape or format by Nikon - heck if there was, I think the price would be quite high!
The only available (Nikon) options for the focal lengths you want are;
Nikon (Nikkor) AF-S 55-200mm f/4-5.6G ED DX
Nikon (Nikkor) AF-S 55-200mm f/4-5.6G ED VR DX
As you can see, the only substantial difference is the VR capability and current (UK) prices puts the VR at a lower price, which is a no brainer as far as choices goes between the two.
Or as Bill suggested, the 55-300mm is only about £90 more ($~140) - depends on your budget and needs of course
