In total we have three lenses, the first one FX format lens and other two are DX format, all the lenses will do AF with you Nikon D5100 or D5000 DSLR.
Lens Ranking based on sharpness (at tele end)
#1 Nikon 70-300mm f/4.5-5.6G IF-ED (eq to 105-450mm when mounted on D3100 / DX format camera)
#2 Nikon 55-300mm f/4.5-5.6G ED VR
#3 Nikon 55-200mm f/4-5.6G IF-ED.
Nikon 70-300mm AF-S DX f/4.5-5.6G IF-ED AF-S VR
The 70-300mm is a Sharp Lens,you get very nice Bokeh, very less Distortion and Chromatic aberration.
Buy Nikon 70-300mm AF-S VR Lens from Amazon || Amazon UK
Nikon 55-300mm f/4.5-5.6G ED VR
Very minor distortion at 300mm, and a little pincushion distortion at mid zoom range.
Buy Nikon 55-300mm Lens from Amazon || Amazon UK
Alert: New Version of the lens available at Amazon.com, It features VRII image stabilization, VR II image stabilization for handheld shooting at up to 4 shutter speeds slower than would otherwise be possible.
Nikon 55-200mm f/4-5.6G IF-ED VR
Buy 55-200mm VR Lens from Amazon || Amazon UK