Larger and less crowded pixel sites that FF cameras typically enjoy are better gathering light (more fine detail) and are less inclined to heat and cross-talk (lower image noise). And FF often are able to use a weaker AA filter (more image detail). More about this below.
Also, to make any particular size print requires less enlargement (magnification) with a FF camera, than it does with a cropper. For example, to make an 8x10 from FF is approx. 8X magnification. The same size print from an APS-C sensor requires approx. 13X mag. So a print from FF should be better. Or, another way of looking at it, the images from a FF are more enlargeable, can be used to make bigger prints... Or, yet another way, due to the greater image magnification needed with a crop sensor camera might be more demanding of quality lenses, because any optical flaws will be more greatly magnified.
However, when shooting small, distant subjects with a telephoto a crop sensor typically has the advantage. A few years ago on another forum several of us got together and tested the theory that a crop sensor camera will "put more pixels on target" to give better results with telephoto work.
We used a 21MP Canon 5D Mark II and an 18MP Canon 7D (original version).... which are close to the same age and at least theoretically similar potential. Using the same lens from the same distance on the same tripod and with the same careful manual focusing to shoot the same subject with the same sharpening and image post-processing.... then cropping the full frame image down to the same exact framing as the APS-C camera. The results were pretty much as expected.... The APS-C camera gave better results every time. It just makes sense, the time you crop a 21MP FF image down to Canon's APS-C (which is slightly smaller than Nikon's... 1.6X versus 1.5X), you're left with equivalent of an 8MP camera! So the cropped FF image offered considerably less resolution than the 18MP APS-C camera so there was a noticeable loss of detail with the cropped FF images. The difference was obvious even in moderately small Internet images. The crop camera won out easily.
This was in spite of the fact that the FF 5DII uses a relatively weak anti-alias filter, while the crop 7D uses a rather overly strong one. The AA filter, in case you don't know, is used to deliberately blur digital images to reduce or prevent "moiré" effect, losing some fine detail and requiring more image resharpening after the fact. (Google "moiré" for more info, if you wish.)
In the end, while the crop Canon camera PS-C format suggests it would have a 1.6X teleconverter effect, the higher IQ of FF partially offsets that. The net result is that the crop camera was more like a "free" 1.3X or 1.4X teleconverter... "extra reach" without the penalty of lost light or any slight loss of IQ due to the added optics, both of which always occur when an actual teleconverter is used.
You might repeat this test with other camera combinations and will likely find some variation depending upon which models are put up against each other.... But I'm very confident that - all other things being relatively equal - when doing telephoto work you are nearly always better off using a crop sensor camera than cropping the images from a FF camera. To get comparable reach with a FF camera, you would have to use much more powerful, bigger, heavier and far more expensive lenses on the camera.
Conversely, for wide angle work, bigger prints, and low light conditions, the FF camera will almost always be superior. (That's why and how I use both formats.)
All this puts aside some other possibly important considerations... For example the Canon 7D has much higher performance autofocus system than the 5D Mark II, making the crop camera far more capable for any sort of action photography. The more recent 5D Mark III got greatly improved AF, though still not quite as good for action shooting as the original 7D. And now the 7D Mark II now has even better AF.
Newer, very high resolution FF models sort of throw a wrench into the works. The 50MP Canon 5DS has almost exactly the same pixel size and density as 20MP Canon 70D or 7D Mark II APS-C cameras. In this case, the croppers are about equal at low light/high ISO work. However, the highest settable ISO Canon offers with the FF 5DS is 6400 natively and expandable only to a relatively modest 12800. The crop 70D offers 12800 natively and can be expanded to 25600, while the newer 7DII has native ISO 16000, expandable to 25600 and 51200. You'll run into similar difficulty comparing 36MP FF Nikon with their 24MP crop sensor cameras.... Or comparing Sony 42MP and 36MP FF models, with their 24MP APS-C models. (Note: Nikon uses Sony sensors in their cameras. Also note: The new, 20MP FF Canon 1DX Mark II goes a different direction with lower resolution on a full frame sensor, which among other things makes it able to offer extremely high ISOs... up to 51200 natively, expandable as high as a stunning ISO 409600! Nikon and Sony both have similar, lower resolution FF models, too.)
So, while FF will generally be better than crop sensor cameras for high ISO work, it depends upon the FF camera's resolution. And, ultimately, you'll have to judge for yourself if any of the high ISOs from either format are actually usable for your purposes.
Larger and less crowded pixel sites that FF camera... (
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