Nikon 50 mm 1.8 lens vs 50-200mm 4-5.6 lens?

Which one:
1. Takes better portraits pictures
2. More sharp
3. Has better performance in low light coditions
4. Has higher value for money

1. Both. It depends on you the photographer.
2. Both. It depends on you the photographer.
3. F/1.8. Larger aperture size than f/4.
4. Value is relative. If you value the benefits of a large aperture size and optics of a prime lens, the 50mm would be better. If you prefer the versatility of a zoom lens and the magnification of distant objects, the 50-200mm would be better. It's a case to case basis. There's no such thing as the best lens overall.

1. The 50mm prime usually would be a better choice, due to the ability to use shallower depth of field. The telephoto lens can compensate for that a bit by using longer focal lengths though, which will give you a blurred background too.
2. The prime lens - prime lenses usually are sharper than zooms of the same price category. That's one of the reasons why people use prime lenses instead of the more convenient zooms. One has to use it correctly though, a lens can only bring its sharpness to bear if the person behind the camera knows what he or she is doing.
3. The 50mm lens, obviously - due to the f/1.8 maximum aperture. Frankly, if you couldn't tell this yourself from looking at the stats of the lens, then you really should read a book on photography. This is absolutely basic knowledge, like "use the gas pedal of your car to accellerate".
4. Apples and oranges, as they are lenses for different purposes. Each offers better value for money in the purpose that it was designed for than the other.

Note that if you use an entry level Nikon camera such as a D3100 or D5100, then you need the AF-S version of the 50mm/1.8 lens, not the cheaper AF version. Otherwise it won't autofocus on your camera.

If you decide to get the 55-200mm Nikon lens, make sure that it is the version with image stabilization (VR). Don't even consider the version without.

4.can't be answered, since it depends on your usage, but if you are looking for a lens to use in low light it has to be the f1.8 lens.

1. Both. For portraits (in general), you not need tele much. But having f1.8 can give you a very soft background effect that you will like.

2. Both can be sharp, it also depends on your skill and knowing the lens limit (like which range of f/ gives you the sharpest images). But again, I will pick 50mm f1.8 as it give you exact shutter speed and it turns out to get less blur images.

3. No doubt, 50mm f1.8 even monkey knows it.

4. 50mm f1.8 is fairly cheap and this is I strongly recommended as 2nd lens to have. (1st lens is 18-200 for general purpose and travel).

so, between 50mm f1.8 and 50-200mm 4-5.6, pick 50mm f1.8. Trust me, you wouldn't disappointed of having a f1.8 lens.