In the enthusiast segment, though, there is a very clear trend at the moment: The importance of the sensor size. We have the very successful Sony RX100 large sensor compact camera sporting a "one inch" sensor, while previously cameras from the same segment typically had 1/1.7 inch sensors.
So why, exactly, is the sensor size important? It does lead to larger and more expensive cameras, and larger lenses, so there must be positive aspects as well to balance this out.
One such positive is bokeh: The larger the sensor, the thinner the depth of focus is. Meaning that the foreground and background will be more out of focus, everything else equal. Read more about it here.
Also, the larger the size of each individual photosite, the better the quality. At least in theory. Hence, one would normally expect less noise and better dynamic range from a larger sensor than from a smaller sensor. To illustrate this, I have taken the same pictures using three different sensor sizes:
From left to right: Nikon 1 V3 (one inch sensor size), Olympus OM-D E-M5 Mark II (Four Thirds sensor size), and Nikon D3300 (APS-C sensor size).
Here is a relative comparison of the sensor sizes:
About the test cameras: Nikon 1 V3 is the "enthusiast" CX size camera from Nikon, with a user optional EVF, and a very deep buffer suited for fast continuous shooting. However, the sensor is already one generation old, and fans are now waiting for the newer sensor, seen in Nikon 1 J5, to appear in an updated Nikon 1 V4. Probably, this camera will be announced early 2016.
The Olympus OM-D E-M5 Mark II is a very feature laden and compact camera. It is pretty much state of the art in terms of image quality within Micro Four Thirds.
Even if the Nikon D3300 is the entry level model, it still has the newest 24MP sensor. So while it lacks in terms of autofocus performance and continuous shooting compared with more expensive models, the sensor is as good as it gets currently.
Here is one scene photographed with all the cameras (click for larger images):
Here are some 100% crops from the images at ISO 200 and 1600 to compare the image quality:
Sadly, it appears that the focus was a bit off with the first Nikon D3300 shot, even if I did use live view and CDAF for the best accuracy. But still, we see very clearly here that the Nikon D3300, with the biggest sensor, retains the best clarity at high ISO. The Olympus OM-D E-M5 Mark II appears to apply more sharpening, which makes the edges look sharper. But some details are lost in the process.
With the smallest sensor, the Nikon 1 V3 starts losing details at ISO 1600. You should avoid pushing the ISO above 800 with that camera.
And 100% crops:
A good test of the noise characteristics, is to lift the shadows. So I did that in Lightroom for all the exposures, by using the RAW file. Here is what they look like with an exposure compensation of +2 (two stops increase):
This comparison was not completely fair, since the exposure with the Nikon D3300 was somewhat lower. This makes the shadows more noisy.
But still, it shows that you have a better chance of recovering shadows with a larger sensor camera, especially at a high ISO.
A larger sensor gives you a thinner depth of focus, popularly called more bokeh, even if that is technically somewhat meaningless.
Also, with a larger sensor, you could expect to get a better high ISO performance. And if you need to increase the exposure in post processing, the image coming from a larger sensor camera is probably going to give you a better result.
On the other hand, a larger sensor also means a larger camera, and a larger lens. I think a nice balance is the Four Thirds sensor size, used in the Micro Four Thirds cameras. The moderate size of the sensor allows the lenses to be smaller and lighter.
The Nikon 1 system, with the even smaller "one inch" sensor, is not there yet in terms of image quality, in my opinion. But give it one-two more generations of sensor development, and I think the image quality should be sufficient for most uses.
On the other hand, there are manufacturers who would like the customers to go for the larger "fullframe" size (36mm by 24mm). Sony has their A7 mirrorless line, and are working hard to complete it with the lenses typically needed by enthusiasts. Nikon also wants to push their DSLR users into their FX ecosystem, where the profit margins are much larger.
Fujifilm are happy with the APS-C sized sensor, though, and are committed to creating the best system around it.