If an iPhone and Canon Mark III both film at 1080p why does the canon look so much better?

If it the same number of pixels should'nt it look the same?

It is NOT the number of pixels but the size of each pixel

Here is how the sensors of the iPhone and Canon 5D, Mark III.

The larger each pixel, the better the colour depth, dynamic range and performace in low light (high ISO)

This is a general statement, since the design of the analogue to digital processor also has a lot to do with those key performance criteria, so it is possible that the same size sensor of one brand may still out perform one of an others.

As well as the pixel area, lens quality also makes a difference in image quality. Most notably, cell phone lenses have poor contrast due to the limitations of making a simple lens. However, for a camera that is smaller than a dime (what's in the iPhone) it does an admirable job.

Because the iPhone has a lens the size of a gnats gonads and the Canon 5D MkIII has a full sized high quality multi element lens.
Because the sensor in the iPhone is the size of a new born baby's little fingernail whilst the Canon has a sensor that is 24mm x 36mm

Larger sensor, better optics and most probably a highly skilled user. Want better video than from a dSLR? Use the right tool, get a digital camcorder.

The output video file will contain 1080 lines per frame.

Each line is made up of a row of pixels and there are 1092 pixels in each row.

So the video from both devices produce the same data to fit the 1080 video standard.

But the sensor in the two devices are very different. The sensor in the iPhone is small. In 1 row it does NOT have 1920 sensors per row. It has perhaps… 150.

This means the sensor in the iPhone takes 1 piece of light and spreads it across about 6 pixels of the line of video.

The Mark III is called a 'full frame' camera because the sensor is big enough that it has 1920 sensors in each row. This allows the sensor to detect a lot finer details and produce pixels next to each other that are not the same.

Add to this bigger sensor, a better lens (and the sensor depends on the quality of light) and the Canon produces a image with a lot more details.