Larger Sensors have some advantages over smaller ones, especially performance at higher ISO numbers (less noise) and the ability to pack more pixels into the same area without loosing too much performance.
In the DSLR range, you are usually confronted with either an APS-C sensor (also called "crop sensor") or a Full Frame sensor (it's called Full Frame because it is of the same size as 35mm film was in the early days).
If you put a 50mm lens on a APS-C camera and then, the same lens, on a Full Frame camera however, you get a very different result. This is because the sensor size is much smaller and therefore it acts as if you just cut out part of the image.
So the problem here is, whenever you hear people tell you "a 50 is a must have" or "you should use a 50mm lens for this or that" what they mean is: a 50mm on a full frame camera!
Now this is something that I found incredibly confusing and somewhat annoying at the beginning.. why doesn't anybody tell you the frame of reference if it's so important?
The reason people liked 50mm lenses from the early days of film on, is that this lens gives you an approximate view that is close to what your eye sees. That's why some people also refer to it as a "normal" lens. To be exact, normal lens is a bit of a range and roughly covers everything from 35mm to about 50mm.
Ok, so now that we've got this confusing bit out of the way let's talk about "focal length eqivalent".
As you can see from the image above, the APS-C photo looks as if we zoomed in with the camera (even though we did not, it's just a smaller sensor that only records part of the image). Given that Full Frame is what everything is related to, we can give a focal length that would look the same as the APS-C image if taken on a full frame camera. In other words, if I wanted to take the same image (50mm APS-C) with the full frame camera, what would I need to zoom in to.
The anwer is: if you use an 85mm lens on a full frame camera, you get about the image you get with a 50mm on an APS-C (meaning: a close up).
Still with me here? I know this is a bit confusing if you never heard of the whole issue.
Now here's the thing. People use 85mm (on full frame, remember) lenses preferably for shooting portraits. That's why many also call them "portrait lenses". And if I say portrait here, I mean something close to a headshot (the head is the main feature in the frame).
Now a 50mm on APS-C gives you the equivalent of a 85mm so you might be tempted to use it for shooting portraits. HOWEVER, a 50mm lens is not the same as an 85mm lens on full frame, it only gives you the same zoom, not the same look! In the image above with the wine bottle i tried to tweak the aperture setting of the camera to make it look close to the 50mm. In reality they have different bokeh and the 50mm has more barrel distortion (which, by the way, you can not completely correct for in post-processing - even though this is a feature of lens correction modules of, say, lightroom).
This is one of the reasons why using a 50mm is not so great for portraits, it bloats the faces due to that barrel distortion the lens inherently has (due to the focal length). The shorter you go with the focal length, the more this becomes apparent until you arrive at the noticeable fisheye effect at very short focal lengths.
Here is a demonstration. I took 3 images of Mr. Foamhead here using the same settings. Once with a 50mm lens on APS-C, once with an 85mm lens on Full Frame and once with a 50mm on Full Frame. I changed the distance of Mr. Foamhead to the camera by moving the camera closer or further away to get the same framing. Can you tell which one is which one?
Now at first you might think there is no difference here. But look closely at the distance between nose and cheekbones, the roundness of the face, the contours and also the out of focus look of the lightstand with the flash on it behind the head.
All were shot at an aperture of 1.8 and I tried to match the lighting as close as I could. Doing this with a model, which I initially wanted to do by the way, is almost impossible. Minute movements of the head, a slight tilt of the jaw and you already have a hard time interpreting the differences between the images. In this case the head did not move an inch and angles are exactly the same (well, as close as possible).
OK, if you're done guessing: here is the solution.
#1 50mm on Full Frame camera. #2 50mm on APS-C camera, #3 85mm on Full Frame camera.
The 50mm on Full Frame really distorts the face and makes it look very rounded (in human terms the person would look heavier than he/she really is). The 50mm on APS-C looks close but you can still see that the face is much more round pretty clearly. Lastly the 85mm gives a rendition that looks much closer to what the head looks like in real life. You can also see that a 85mm 1.8 on full frame has more bokeh as the 50mm 1.8 on APS-C (look at the lightstand with the flash).
Here are some measurements if you are into data:
Here I measured the distance from the middle of the face to the cheekbone and the tip of the nose to the top of the head to judge roundedness of the face. From the ratios you can also see that the face is less rounded and therefore less distorted than with the 50mm lenses.
Does this make 50mm unuseable for portraits? No.. I would definitely not use them on a full frame sensor, it gets better on an APS-C camera but my recommendation is definitely getting a longer focal length for portraits, also on APS-C.