Is the Nikkor 50mm f/1.4 better than the Nikkor 50mm f/1.8?

Is the Nikkor 50mm f/1.4 better than the Nikkor 50mm f/1.8?

No. F/1.4 is an useless setting to me. It delivers extremely soft pictures and it's hard to get both eyes in focus. Even at f/1.8 is hard to get both eyes in focus depending on the shoot. I never go below f/1.8 and I only use f/1.8 when I want very shallow depth of field. I don't usually go below f/2.8. Even f/2.8 will give you enough depth of field in most cases.
The Nikkor 50mm f/1.4 is heavier and more resistant than the Nikkor 50mm f/1.8.
That's where the price difference between those two lenses come from.

Yes

I don't know what you mean by better; I do know that one is FASTER than the other. I've actually used both lenses and I kept the 1.4 after shooting in a low-light situation where I was unable to use a flash. I used it for college team portraits for yearbooks (back in the days of film, and now with my FX camera) and the results were spectacular but I was not shooting at 1.4 because of the fine weather, great skies and fantastic late afternoon sunlight. There's really not much differences in terms of lab spec comparison tests (see: http://www.adorama.com/...18-or-f14) but the 1.8 is considerably less expensive than the f/1.4 and far less expensive than the manual Nikon 50mm f/1.2 (the fastest lens in production, and the very best for quality image when set at f/2). IF you're not gong to be using it often, or on a regular basis, go with the f/1.8 and enjoy it when you do use it; the image quality will certainly surprise you in pleasant ways.

Trust me when I say I'm not being sarcastic, but if you have to ask you're not ready. I'd recommend the 50mm 1.8G because the 1.8D may not work with your autofocus on your camera depending on which model it is. Having a good prime lens is amazing. You're gonna love it, have fun & good luck!

If you mean better because it's wider - then the answer depends on what you are using it for. As with anything, "better" is a highly subjective word.

If you are taking photos of people, then setting the aperture at f/1.4 or f/1.8 will produce such a shallow depth of field that you might not be able to get the persons whole face in focus - unless they are directly facing the camera. The minute you tell them to sit sideways, and turn their head even slightly to one side, the depth of field will be so shallow you will have one eye in focus, and the other out of focus.

When I shoot portraits with a 50mm on a cropped sensor camera, I rarely shoot wider than f/2.8.

If you are using the 50mm in extremely low light situations, then using wide open apertures will obviously let more light into the camera, so in some situations wide apertures can be useful. In most general photography however, you will find that wide open will not work well for many subjects. In fact really wide apertures are a distinct disadvantage for some subjects such as landscapes, where f/8 to f/16 is the optimal aperture for sharp images.