There are both advantages and disadvantages to so-called "full frame" cameras.
Advantages:
FF has potential for better image quality. Among the most basic reasons... a bigger sensor simply means less enlargement to make any given size of print. For example, to make an 8x10 (or 8x12) from a FF image is about 8.5X enlargement. From the APS-C crop sensor camera, around 13X enlargement is needed to make that same size print.
Another way of looking at it... you likely can make bigger prints from a FF capture, than from an APS-C. The difference in quality may not be very noticeable in an 8x10 or at Internet resolutions... but would be more obvious by the time you're making 16x20/16x24 and larger prints. Or, yet another way of looking at it... the FF image is more "crop-able".
Larger pixel sites possible with a FF size sensor gather more light, so can record more detail.
And the much larger sensor area can make for a less crowded sensor, which in turn helps reduce heat generated and cross talk between pixel sites, both of which make for less image noise and higher usable ISOs. For example, 18MP APS-C cameras I use have about 54,000 pixel sites per square millimeter. Compare that to a 21MP full frame camera I also use, that has less than 25,000 pixel sites per square mm.
A less crowded sensor is less prone to moiré effect, so can get by using a weaker Anti-Alias filter. To offset moiré, AA filters actually blur the image ... which is then re-sharpened. A weaker AA filter, less blurring and less re-sharpening with FF, preserves more of the original detail in the image.
A different way of looking at sensor pixel density... If the same pixel size and density is used in both cases, the FF camera will be much, much higher resolution. Canon's 20MP APS-C EOS 70D and 50MP FF EOS 5DS have about the same pixel pitch.
Wide angle lenses don't need to be as extreme designs with FF, so potentially may be more easily corrected.
Disadvantages:
FF cameras cost more to buy, because they cost more to make. For example, a common "wafer" used to make sensors can accommodate 80 APS-C size... or 20 FF size. So in raw materials alone, a FF sensor costs 4X as much to make.
Also, those wafers have flaws that will cause some number of the sensors made from them to be unusable. Let's say, for example, that there are two such flaws in on a given wafer, so that two of the sensors made from it are unusable. If it's being used to make APS-C size sensors, that's a 2.5% rate of loss. But in the case of FF, it's a 10% rate of loss!
Some other components of a FF camera need to be scaled up to match the sensor size, too. The shutter, mirror, focus screen, pentaprism and other optical viewfinder parts all have to match the larger sensor size. This often makes for a bigger camera, as well as higher cost.
Often FF cameras produce significantly larger image files, which either slow down shooting speeds, or call for larger image buffers and more powerful processors to be able to maintain high frame rates and long bursts of images.
Larger moving parts (mirror and shutter) also make the FF camera more prone to internal vibrations and likely to be noisier in operation. It also often makes for slower flash sync speeds (FF 1/200 vs APS-C 1/250 or 1/300, is common with portable flash... FF 1/120 vs APS-C 1/160 or 1/200 is common with studio strobes).
FF cameras also need FF-capable lenses, which may limit choices to some extent. (Compared to APS-C cameras, which in most cases can use both FF-capable and crop-only lens designs.)
Lenses for FF need to be able to produce a bigger image circle, in order to fully and reasonably evenly cover the larger sensor, which makes for bigger, heavier and often more expensive lenses, too.
Much bigger image files produced by a FF camera may be "overkill" for many purposes (such as 8x10 prints and Internet image sharing). Computers to work with the larger images will need to be more powerful and to have more storage space.
Telephoto lenses, in particular, have less "reach" with FF, than they do on a crop sensor camera. This is partially offset by the differences in image quality, but there is still some advantage to crop sensor cameras with telephoto lenses. For example, I shoot a lot handheld with a 2.5lb, 300mm f4 lens that costs about $1400 on an APS-C camera. In order to get as tight an image of a distant/small subject with a FF camera, I'd need to get out an 8 lb., $9000 500mm f4 lens and a $1500 tripod to support it!
Myths about FF
Depth of field doesn't actually change with different formats. Only lens focal length, lens aperture and distance to the subject change D0F. However, many think it changes with FF because in order to frame a subject with FF the same way you did with a crop sensor camera, you either need to move closer to the subject or use a longer focal length lens, or a little of both.
Personally, I use both FF and crop sensor cameras. The urposes I use each digital format for are similar to what I did with 35mm film and medium format film cameras some years ago. What's really nice about digital is that the two formats can largely share lenses and other accessories. Often with different film formats, systems weren't interchangeable to much extent.
I'd estimate that I use my crop cameras about 10X as much as my FF. That's just due to what I shoot... a lot of sports/action, for which I prefer the croppers.
In my opinion, FF is sort of a fad right now. It's arguable that a lot of FF buyers and users really don't need it. So do, sure. But crop cameras, used right and not "pixel peeped" overly critically on computer monitors, can and do serve many folks just fine.
There are both advantages and disadvantages to so-... (
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