In a camera you have a sensor. That sensor turns light into numbers; and then a computer, in the camera or out of it, 'paints by numbers' to make a picture on a screen or piece of paper for you to look at.
Compact cameras have little sensors; bridge cameras have bigger sensors, DSLR's bigger sensors still.
Bigger the sensor, the more light falls on it, the more acurately it can turn light levels into numbers.
Pixel count.... how many individual receptors are etched onto the sensor. More receptors, the more different points in a picture can be sampled, more detail the picture can 'resolve'
Now we get to the lens. Bigger the lens, more light will pass through it, more light will fall on the sensor, more acurately it will tend to make a picture.
BUT... depends on the lens... every time light passes through a bit of glass, some light will be reflected rather than pass through, and then the more the lens 'bends' the light, more likely it is to defract, like a rainbow through a rain-drop. More bits of glass there are in a lens the more chance that you will suffer bigger transmission losses and more refraction or internal refrection which as far as pictures go means distortion.
Good lenses then, are more efficient, and pass as much light as they can, without distortion. Poor lenses, are less efficient and can distort your picture.
Its easier to make a big lens than it is a little one.
But that is only half the story... becouse ZOOM range is utterly independent of lens quality. Big zoom does not mean BETTER lens. In fact more likely the converse. To change the image magnification, more has to be packed into the lens, even more so on a compact camera where the zoom is motor driven. More moving parts, more complexity, less durability or robustness, and generally the more expensive it is to make it efficient and accurate.
The Nikon D3000 is a Digital SLR. It has a crop size sensor, about 25x16mm, with a resolution of 10Mpix, and an interchangeable lens.
The Cannon SX260 is a compact camera, with a sensor probably, oooh... 8x4mm or so.... and a resolution of 12mpix, and 10X optical zoom lens.
Cannon Compact costs £200, Nikon DSLR costs about £250.
They are totally different cameras intended for different uses and markets.
Ultimate image quality is not a priority on the Cannon Compact; its a point & press pocket camera; that's supposed to be quick and easy to use, but give pictures that are 'good enough'.
Its hampered by its small sensor, and the higher pixel count wont make its pictures any better unless the lens can give them the light and detail in that light it needs. Being a compact the lens is small, so its got less chance to be so wonderful, and for the price, its going to be harder to make a lens 'as good', even more so stretching the manufacturing cost to offer 10x zoom range, rather than maybe 3x, which is what my kids compacts have.
So, out of what you are paying, most of the money has been used to make it small, and give it big numbers... it probably isn't a brilliant camera and unlikely to be wonderfully durable and able to take a few knocks.
BUT it is convenient and easy to use, and the image quality should be 'pretty good'....
I have an ancient 5Mpix compact, which doesn't even have a lens, let alone an optical zoom..... even THAT is 'good-enough' for a lot of photography I have done in the last ten years, and for most purposes I have to re-size down pictures from camera for any practical use, like display on forums or face-book!
My Nikon DSLR is a lot more versatile, and I can do a lot more with it, and I would hope that its at least as robust as my kids compacts! Its pictures are far more detailed and higher resolution than my old compact, or those of y kids or other-half's bridge..... but for most purposes that just means I have to shrink them a heck of a lot more to use them!
I dont have the zoom-range of my O/H's bridge, without changing lenses, I have just about the same range as my kids compacts... but I cant stick the thing in my pocket very easy.
So.... features you have considered 'important'... basically aren't.. whats important is what you want the camera for?
Do you want the versatility of a camera you can take more manual control of and use interchangeable lenses, and maybe has greater range of ISO settings and other features.....
Or do you want a good, all in one, stick it in your pocket, dont have to think too much, point and press camera?
The 3 cameras listed all have completely different features and only you know what ones are important.
