I assume you have some kind of zoom lens now, and it probably covers those focal lengths. Rather than have us tell you what focal length we prefer, it might be better if you set you lens to 50mm and tried shooting some of the subjects you like, then try it at 35mm and make your own choice.
One reason I say that is that, really, I'd choose the 50 for portraits and the 35 for street. So if you are going to get just one of them, you really need to figure it out for yourself based on your tastes.
I used to have the 35 1.8G as my prime on my D80. For a short tele, I used a 60 2.8D. The 35 1.8 became a 52/53 1.8 and the 60 2.8 became a 90 which would be the same on the D7000. For street, you would be better off using a 24 2.8 and the 50 for portraits as the 50 becomes a 75. Charlie
I was faced with the same decision several months ago, and went with the AF-S 50mm f/1.8 G. It's a great little lens, but in retrospect I think I would have gotten more use out of the AF-S 35mm f/1.8 G DX. The 50 is too much of a one-trick pony - it's great for portraits on a DX camera, but it's a little too long for general use.
That said, if I ever go FX, I already have a nice 50mm to use.
I just struggled with this decision on my D7000. I will echo what Jon and Scott suggested and take a look at what focal lengths you have been shooting at. I did that myself and found a large amount of shots in the 35mm area. Being stubborn, having had the 50mm in my mind and knowing I would want to add a FX or film camera eventually, I bought both last week.
I played with both over the last week or two, mostly family snap shots at Thanksgiving and some of the dog asleep, a bush or two in the yard. Over all I think the 35 is more useful on the DX D7000. I do think the 50 is a little faster to focus, but it is a little tight for some shots. I think they are both great lenses!
I have both, and I use them both to shoot basketball in dark gyms on a D7000. If I could only have one for this use, it would grudgingly be the AFS 50 f1.8G, as I probably use that FL more often for the reach. However, if I could only have one of these for general photography, it would definitely be the AFS 35 f1.8G.
Here is a suggestion. Get the 35mm, as I believe it is more versatile for your use. It is also less expensive than the AFS 50mm. Then, buy a used AF 50 f1.8D from KEH, probably for about $50.00. This lens is tiny, well made, and very sharp, even wide open (I know, I had one for nearly 15 years). Unless you are shooting action, it is indistinguishable from the newer AFS version. It auto-focuses slower than the AFS version on the newer bodies, but I never noticed this for any use other than basketball in very dark gyms, at very high ISO.
I sold my old 50 AFD after I got the newer one, because it was redundant, but I'd still have it if I didn't need the faster AF. This is an economical way for you to get BOTH focal length lenses for less than the cost of the new AFS 50 f1.8G.