The two softwares are very different from each other and you cannot really say either or. Nikon Capture (NX is the latest version) is, i would say, primarily a RAW -> JPEG/TIFF conversion. As such it allows you to do adjustments to your photo (contrast, brightness, saturation, colour, curves etc etc) including some stuff that comes close to dodging and burning. Adjustments can be done to the RAW file BEFORE conversion and also to the jpeg files. But all adjustments are written into the RAW/jpeg file. NX is rather cumbersome to use with a lot of controls all over the place. Capture allows you also to operate your camera tethered and to load custom curves to your camera. Capture is specifically for Nikon cameras
Now Photoshop is a general graphic software not just for photography. It allows you to convert RAW to jpeg as well (through Bridge). you can do similar things as in Capture however not to the RAW file direct. In some cases it is more elegant in some cases not. In any case it is more versatile, specially with the use of layers that give you much more freedom in modifying your files.
before choosing one or the other you should understand what you want, because there is other software around as well.....
RAW conversion: NX is definitively better than photoshop, but then there are others such as Capture 1, Lightroom (currently you can download free beta version from Adobe), RSE (Rawshooter Essentials) just to name a few
Exposure correction: again i would guess that NX is doing a better job than photoshop but Lightroom (RAW and Jpeg) and RSE (RAW only) do a much better job in this
Actual graphical work on the photo such as dodging, burning, grey layers etc etc.: this is where you want to use Photoshop but also there are alternatives. Dont have the money? Download The Gimp for free! This software allows you to do almost the same as photoshop (not as refined though) and it is free....