Comparing the two lenses for an APS-C sensor:
Leaving out cost as a factor, EF 35mm has the following advantages:
Even after these advantages why do some people prefer 50mm as their 2nd lens to kit lens?
The 50mm is a simpler design compared to the retrofocus 35mm, as such it's much cheaper and slightly sharper.
50mm on an APS-C body corresponds to about 80mm on full frame, which is a very popular focal length for portraits. The kit lens covers the wide angle needs so sometimes a longer prime makes a good companion, for tighter compositions with blurred backgrounds.
Having a single focal length of 35mm is not that much more useful than having a single focal length of 50mm, compared to having a prime plus a zoom.
f/2 vs. f/1.8 clearly isn't an advantage for the 35mm. The most you can say is that the advantage of f/1.8 over f/2 is small enough that it rarely matters much. There's no room for question that the 50mm wins in this respect though. The only question is whether it's a big enough win to care much about.
43 vs. 31 degree FoV is (IMO) pretty close to neutral. A wider angle may favor your shooting style, but that's certainly not universal. If there was a preference here, I'd say it leans in favor of a longer lens, especially for beginners -- beginners are often shy about approaching subjects as closely as would be ideal; a longer lens can help compensate for that to at least some degree. Of beginners pictures I've looked at, I'd say too loose of composition was a problem at least five times as often as too tight of cropping.
Making the total kit compact again seems to be mostly treating your own shooting style as how the world works. If I had to use APS-C with only two primes, I can see 50mm as one of the choices a lot more easily than 35mm. 50mm is long enough to use as the "long" lens for quite a few purposes (i.e., most things other that sports and wildlife). You can pair it with, say, a 24mm and cover quite a bit reasonably well. With 35mm, you nearly need both shorter and longer focal lengths, so your minimum becomes a three-lens set, so the 50mm wins again.
In the end, I think it mostly comes down to shooting style -- both what sort of subject matter you like to shoot, and how you like to shoot it.
I should probably add that on APS-C, most primes never really feel "right", at least to me. Maybe it's just because I shot film for so long, but none of them ever seems to really give the right "feel" for most pictures. For example, portraits with a 50mm either end up a bit loose or else overemphasize people's noses too much. With the 85mm, you end up having to back away so far that even though the subject fills the frame, there's much less feeling of immediacy and connection -- to me it's more like a really good wildlife photo than a portrait.
I suppose the cost factor is a heavy one here. The 35mm lens model costs thrice as much as the 50mm lens.
50mm F/1.8 is recommended due to the practical FOV (on full frame), and the aperture gives you a fast lens, you can use indoors with low light, and you also get to play around with narrow depth of field which is nice for focusing on a subject and blurring the background. However, in your aps-c camera you need 28mm or 35mm to get the practical FOV close to 50mm on fullframe. Then there's also the matter of perspective "distortions" related to the FOV, which is important in making faces look natural. The 28mm might be on the lower threshold for that. But the 35mm will make the lens less practical in every day shooting (I once used the 28mm on a holiday and found that even that was slightly too narrow).
Have a look at this 28mm option, which I actually choose as my "fast fixed focal lens":
It has the same FOV as a ~50mm on fullframe (on the low side, while 35mm is on equally close on the high side.), fast USM focus, it also has a better "bokeh" with 7 blades and it is razor sharp.
Try shooting with both eyes open.
50mm, as a focal length isn't just about field of view, although that's how most people judge a lens as being "normal"--the other things to consider about the 50mm focal length itself is that the magnification/perspective of the lens are a relatively close match for how the human eye sees. If you mount a 50mm lens on a dSLR--whether full frame or crop, and you shoot with both eyes open, the view between the non-camera eye and the camera eye will match. With a 50mm lens, composition is simply a matter of framing.
If you use a longer or shorter focal length, the lens itself will change the magnification/perspective. What you see between your camera and non-camera eye is no longer the exact same scene. Composition in these terms requires not only considering framing, but also translating for the focal length used. The 50mm lens, for some folks, is the most 'neutral' of all focal lenses. You don't get the perspective "compression" of telephoto, nor the "expansion" of wide angle. Objects are the same size and shape as with the unaided eye.
I shoot micro four-thirds, which has a 2x crop factor, so there's no way that my m.Zuiko 45mm f/1.8 could count as "normal" or a 50mm-equivalent lens (it's a 90mm equivalent), but I often prefer using it as a walkaround lens, because a) I cotton naturally to short telephotos and b) composition is all about framing. What I see through that lens and through my unaided eye match. Despite the fact that my 20mm f/1.7 lens is nominally closer to "normal", FoV-wise, it is still really a wide angle lens and behaves accordingly, and everything through the viewfinder is smaller and farther away than I see it with the non-viewfinder eye.
