There are often questions asked about what is the difference between a “full frame” sensor on a camera and a “cropped” sensor. This will hopefully explain the differences.
A “Full frame” camera has a sensor the same as size as 35mm film, being 36mm x 24mm. The film was 35mm wide and with sprocket holes etc allowed the 24mm width and it was very popular over a long period of time.
APS stood for Advanced Photo System and the idea was that you could take portrait, landscape and panoramic images with the same film by selecting a switch on the camera before you shot. It never really took off.
APS-C is a format 22.5mm x 15mm so it is the same aspect ratio as full frame (3:2) but much smaller in each direction. This means that for a given lens the image will appear 1.6 times bigger in each direction or 2.5 times bigger in area overall.
There are some advantages to this. The camera and lenses can be smaller and distant objects will appear bigger. Because the sensor is small the moving parts like shutter and mirror can also be smaller and so a faster frame rate can be achieved. These advantages also apply to most point and shoot cameras.
The disadvantages are that you lose wide angle capability and the lenses no longer work as they should for the focal length they are made for. By that I mean a wide angle lens is no longer wide and a portrait lens, if you even have the space, puts you too far from the subject.
Because the sensor is smaller the pixels or picture elements are smaller and closer together for a given resolution so this makes the images noisier. All imperfections from the lens or dust etc are also magnified 2.5 times more.
When you print an APS sensor to A4 you have to magnify the image from 22.5 to 297 mm or 13 times in that direction. So your A4 print is basically 169 times as big as what you captured. It had better be good.
Your A4 print off a full frame camera is magnified from 36 to 297 so its magnified 8 times each way or 64 times. That’s a pretty big difference in potential image quality.
So yes, a full frame camera, ALL OTHER THINGS BEING EQUAL, does take better photographs, but you may need to magnify them up to see. The differences in usage however are apparent as soon as you have look through the viewfinder.
If you step up to medium format the same thing happens again. An A4 print off a 645 camera (56 x 42mm) would be magnified from 56mm to 297 or 5 times, so roughly only 25 times.
With cameras, if image quality is the criteria, for a given brand and lens, bigger is better.
If you photograph architecture, landscapes or portraits you will almost certainly be better off with a full frame camera.