The compact cameras can offer decent quality, but where they struggle, is with low light.
With the nikon one cameras, you will basically have trouble going above ISO 800, but on top of that, unlike larger sensor cameras, these smaller mirrorles cameras will have noise at all ISO levels (including color noise) while with a larger sensor camera, you will generally only be stuck with some luminance noise at low ISO's and a small amount of color noise at higher ISO, this makes sample based noise reduction easier, as many advanced noise removal programs which go beyond lightroom or other raw processing cameras, they can remove luminance noise rather easily, but color noise is always destructive , as the characteristics of color noise change based on the the light levels of each pixel on the sensor.
With aps-c sensor camera, you can generally control the noise very will up to ISO 1600 before you start having difficulty with color noise.
Many photographers who upload their photos on line, will often upload low res images, e.g., 1600x resolution when the original photo was around 5000x, so when they show the low res image, things will look clean and sharp, but the original image will be grainy at 1:1 zoom.
Other than that, those cameras tend to lack audio connectors, and phase detect auto focus, which means that focusing will be very slow in low light, and tracking may not work at all.
When it comes to entry level DSLR's if your main focus is still images, then something like the nikon D3200 (or 3300 if available) offers the best image quality for the money.
If you are focused on budget video, then the t3i and up are best as they work well with the advanced features of the magic lantern firmware. including the ability to record raw video from the camera. (this offers a similar dynamic range to the RED epic) though you will be spending at least $ 100 on an SD card as anything less than the 95MB/s write ones will cause choppiness (unless you are okay with recording at a lower resolution) (even with the fastest SD card, it may still have some issues with 1080p raw, so some experimenting will be needed where the resolution is slightly lowered little by little until the card is no longer overrun)
for example http://www.youtube.com/watch?v=0fGIIAQXXxQ
raw video comparison on the t3i http://www.youtube.com/watch?v=il0qu1CTjrM