I have 3 cameras: Sony NEX, Nokia 808 Pureview and Lumia 920. The NEX having APSC sensor is technically capable of image quality equivalent to entry-level DSLRs. However, under good lighting conditions, the 808 is so good in 41MP, that it greatly outresolves the NEX. Therefore, I actually prefer shooting with the 808 more than the NEX (in good lighting conditions). The amount of details and sharpness is incredible.
Low light images are a different story.
The 808 is also capable of taking great low-light pictures in downsampled mode, although overall the NEX still performs better in low-light thanks to the large sensor. The 920, however, performs very well in low-light - I will say it can even outperform the 808 in situations where the Optical Image Stabilization can help to keep the shutter open longer. I have no difficulties shooting with 1/3 seconds exposure at ISO 100 with the Lumia 920. The 920's OIS, and the 808's 41MP large sensor, are essentially complementary features. So combining both features into the Lumia 1020 will, I strongly believe, be a huge improvement especially when shooting in low light. Imagine having all your shots (daytime and night time) all taken with base ISO 100?
A further comment about the NEX's OIS. Although the NEX also has Optical SteadyShot (where the OIS is located in the lens rather than camera body), it is nearly impossible for me to take pictures handheld with shutter speeds slower than 1/10 seconds. This is possibly due to the weight of the device. Many low-light shots had to be taken at ISO 1600 or above. In contrast, I can shoot at 1/3 seconds exposure with Lumia 920 relatively effortlessly. So when comparing low-light capabilities, although the NEX has far larger sensor size, it may require images to be taken at faster shutter speed, which means you need to use higher ISO setting to offset this, which in turn means you get more noise.
Of course, the NEX gives you a lot more possibilities. You can change to brighter lens, fisheye, macro, telephoto lens, etc. I use a third-party f/1.8 55mm lens together with the NEX, the bokeh effect can never be matched by any smartphone camera. But this means spending a few hundred dollars more on additional lens. With just the kit lens, I find that the difference in image quality between NEX and 808 is not that great. At least not great enough for me to justify carrying an extra (and relatively heavier) device everywhere. Of course technically the NEX is still a better camera overall. But to me, the 808 is more than good enough to use 95% of the time. The only 5% that I use the NEX is for very special occasions.
To put this into perspective, my previous phone was the Nokia N8. It is still considered a good cameraphone by today's standards, but my usage of N8 and NEX was probably around 50%-50%. This was mainly because the quality difference between the N8 and NEX is still quite significant. With 808, the gap is a lot smaller which resulted in the NEX sitting in the cabinet most of the time nowadays. The 808 is really that good.
It is cliche that the best camera is the one you have with you. I find this to be absolutely true, magical moments of inspiration can happen anytime, anywhere. By having an awesome camera with you all the time, it will really expand your horizon, and you will find yourself taking more and more pictures. This will become a hobby that you can indulge ANYTIME, rather than one that requires some planning in advance (taking out a DSLR must be a deliberate decision). As you get more and more into it, perhaps you can then consider more specialized equipments possibly even higher-end DSLRs with good lens. But I will recommend the 1020 for starting out a hobby for the simple reason that it will give you a deeper appreciation for photography once you start taking lots of routine pictures with it.
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