Which telephoto zoom lens?

I'm confused with these two lenses

AF-S VR Zoom-NIKKOR 70-300mm f/4.5-5.6G IF-ED (4.3x)
or
AF-S DX NIKKOR 55-300mm f/4.5-5.6G ED VR
price isn't an issue, but performance sure is. I even heard that the 70-300mm zooming capabilities increases with a DX body (not sure though).
i have a D5100.suggestions please.

Buy the 70-300mm if you think you might go with a full-frame Nikon in the future. Another consideration is this lens has internal focusing which means the front element doesn't move. This feature makes using a circular polarizer or graduated nutral density filter much easier. This lens also focuses slightly faster than the 55-300mm zoom.

Your D5100 has a 1.5x "crop factor". On your camera the 70-300mm will have the angle of view of a 105-450mm lens on a 35mm film camera or full-frame DSLR.

" i even heard that the 70-300mm zooming capabilities increases with a DX body (not sure though)."

Yes, due to the 1.5x crop factor of the D5100 it acts as a 105-450mm lens would act on a full frame or film camera. But EDWIN leaves out one important bit of information - this crop factor applies to All lenses that one uses on that camera. So the 55-300mm one also would act like a 82.5-450mm lens would do on a full frame or film camera. Since the crop factor applies to all lenses that you use on that camera, you basically can completely forget about it unless you need to compare the angle of view that a lens gives on different types of cameras. It will only confuse you. If the D5100 is the only camera that you have, then e.g. 100mm will always be the same as 100mm on any other lens.

If money isn't an issue and you are comfortable with a 70mm wide end, definitely go for the 70-300mm one. The 55-300mm one on the other hand is cheaper and having the wider end may save you from a number of lens swaps.