While comparing Nikon 85mm f/1.8G and 50mm 1.8G, I found the former to be quite a bit costlier. The differences, as I find, are obvious ones because of the focal lengths, e.g. angle of view, dimension, weight etc. All those don't apparently justify for the higher price tag. Is there any crucial/must-have feature the former offers which the later doesn't?
You seem to be under the misapprehension that all lenses should cost what a 50mm f/1.8 costs. The 50mm lens is actually the outlier. The focal length lends itself to simpler designs.
An 85mm lens, to achieve f/1.8 must have glass that covers an aperture opening of 85mm/1.8 => 47.2mm vs. a 50mm/1.8 => 27.8mm. So it requires bigger glass elements throughout, to begin with. It will need additional help with chromatic aberration and distortion correction for the longer focal lengths, so additional elements.
50mm f/1.8 diagram:
85mm f/1.8 block diagram:
The cost isn't arbitrarily higher. It has more materials and design going into it.
In terms of non-obvious features, 85mm is not only going to give you a tighter framing and a narrower field of view and more "reach", but also a shallower depth of field, and possibly better corner performance on full frame. And on full frame it's an amazingly good fit for portrait photography. Less so on a crop, where it's a little too long for framing anything other than headshots.
The price difference is most likely based on the optical design. An 85/1.8 lens will most likely have more elements and larger diameter glass on the outer side.
In general, if you are choosing between 50 and 85mm for portraits, make sure that the lens can focus close enough to do a headshot, that you will be able to properly fit your subjects in the frame in your typical room/studio (85mm will require more distance, could be a problem in small rooms, especially with APS), that the lens has satisfactory looking background blur and does not exhibit nasty chromatic aberrations.
Also consider possible higher cost of ownership of the 85 - if the lens has greater filter diameter, you will pay more for your filters.