You can pick one of three possible answers to this question, all of which are accurate.
The first answer is that
any camera used within its limitations is capable of taking superb photographs. As such, any camera is as good as any other. Don't worry about it; just get out there and take photographs.
The second answer is that
all cameras of the same type and in the same price range will take photos of roughly the same quality. There are differences, but you'll have to look pretty hard to see them.
The final answer is that no,
not all cameras are equal. There are enormous differences between cameras, and some of them are detailed below.
- Optics. Some lenses (and for those cameras with built-in lenses, cameras) will be sharper and have fewer technical defects (like chromatic aberration) than others.
- Metering. Some cameras have far superior light meters to others; Nikon's "matrix" evaluative metering system is alleged to be among the best here. Spot-meters and center-weighted meters as found on pre-80s 35mm film cameras will result in less accurate exposures than a modern evaluative metering system.
- Sensors and firmware, on digital cameras, vary hugely from camera to camera. Some sensors have less noise and more dynamic range (able to accurately render a wider contrast range) than others.
None of this should concern you if you have a camera already; refer to the first, and best answer on this count. In any case, a technically flawless photograph is not the same thing as a great photograph, or even a good one. Someone with an eye for colour, light, shape and texture will make a far superior photograph on a cheap point-and-shoot camera than someone without the eye for such things shooting the most expensive digital SLR available.