Image sensor size matters! And this can even be listed as the only thing which makes a DSLR capture better quality images than compact cameras and mobile phones. Well, there are many other facts, still its safe to say so.
Take an 18MP image sensor on a DSLR and a compact camera. Just as a picture is, an image sensor is made up of pixels too. Thus an 18MP sensor will have 18 million pixels squeezed in it. But a DSLR has a bigger sensor, meaning larger surface area, when compared to the compact camera. Now devide the whole surface area in to 18 million equal parts. DSLR will be having larger pixels, which means it can collect more light, which further implies better detail and quality. Besides that, a larger image sensor allows to bring more dramatic effects in the captured image like a 'boque' (fading out the background totally with keeping the foreground alone in sharp focus; though it is possible with a compact camera, the outcome is way too awesome with a digital single lens reflex camera having a large sensor). Be it RAW or Jpeg, the amount of light matters!
Mirror less cameras are provided with either electronic viewfinders or a non TTL viewfinder. A through the lens view finder is the fastest viewfinder, being not electronic but straight from the lens. An electronic viewfinder can get sluggish sometimes to show any change in the scene that is being shot. A non TTL viewfinder doesn't exactly show what the camera sees as in a TTL type. Without a mirror, only autofocus possible is contrast detection type which is too slow when compared to the phase detection type in DSLRs. Besides all these, a TTL gives a feeling that we see exactly what the camera does.
A word on image sensors
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