I have D90, which one is good 50mm 1.8f or 1.4f lens?

I have Nikon D90 camera body, i'm planning to buy a prime lens. I have two options 50mm 1.4f and 1.8f. I read there will be no much difference in image quality. Does these lens work with DX format well? Which lens i should buy? Any other lens to consider?

The 50mmf/1.4 D or G as well as the 50mm/1.8 D or G will work perfectly on your D90.

If you do a LOT of portraiture and low light work, then going for one of the 1.4 ones might make sense, as these reach their sweet spot of optimal sharpness wider open than the 1.8 ones, e.g. At f/2.4-2.8 whereas the 1.8 versions would have to be stopped down to f/3-3.5
This is only worth the extra price if you really make lots of use of it. One has to look really, really close to notice a difference, and to take direct comparison test chart shots. Otherwise the 1.8 ones will perform just fine at half the price.

Edit:
As a further note, these lenses are both available in D and G versions. The G versions are newer and have an internal autofocus motor. For your D90 that's not really a big issue, as it has its own, and likely all your future DSLRs will have one too if you're accustomed to this level of cameras. The G versions with AF-S focus faster and perhaps also a little bit more accurate. The older D versions are cheaper and have an external aperture ring. This one can be a big advantage if you ever want to use extension tubes for macro purposes. With an aperture ring you then can use $10 extension tubes without electronic contacts, instead of the $150 ones with electronics. Otherwise you wouldn't be able to control the aperture with the cheap ones. Hence it may be a good idea to have at least one lens with aperture ring.

They are both FX lenses, but will work perfectly fine with your D90. The f/1.4 lens will let a bit more light in than the 1.8, but otherwise neither is a bad choice.

I use the 1.8 with a D90 and works great.

There's a whole world of difference between that half step improvement. The f/1.4 is simply marvelous but if your budget is restrictive, the f/1.8 will absolutely be enough. If you want a closer to the eye's angle of view, consider the 35mm f/1.8(?).

Sigma 50mm f1.4 is one of the best 50mms available. Better than both Canon and Nikon 50mm 1.4 and 1.8.