larger pixels meaning you can shoot in lower light or lower ISO noise. Transitions between shadow and light more refined. but youl lose the crop factor on the lens so everything will look farther away with the same mm lens as apposed to the same lens on a crop sensor. Transitions can be partially dealt with in editing. I am considering a FF myself to take my shots to a slightly higher level, but as most will tell you FF is more costly, as are the lenses, and heavier bodies. And youl want to get a good one, read plenty of reviews.
all IMO of course

As I read the responses, I feel many are "sarcastic," and really do not answer your question. First, let me say, one can take good photos with most any camera, I have heard it said, "the camera does not make the photographer, the photographer makes the camera." That is true to a certain extent. But, the bottom line is, a full frame camera will produce better photos! Since the sensor is larger, it captures light better, thus making full frame cameras better in low light situations. Since the sensor is larger, a full frame camera can capture pictures that are more crisp, and sharp. I recently obtained a Nikon D3, and the quality of the photos are so much more superior than the photos of my D7100. Photos taken at ISO 6400 have less noise with the D3 than photos captured with the D7100 at ISO 1600, and less noise equates to sharper detail. I am the same photographer, so the difference in photo quality MUST be the result of the camera. So, yes, better equipment will produce better photos, IMHO. And yes, the D3 is a beast of a camera, heavy. But, when I mount my Nikkor 200-500 mm lens on it, the balance is unbelievable, and I can shoot handheld, and I am 73 years old. Now, I would not want to be on a 5 hour shoot, hand holding that combo the entire time. But, for my style, I can hand hold and get excellent shots.

There is an urban legend that states that more megapixels is better if you are making large prints. Apple may not have gotten the memo when they ran their ad campaign for iPhone 5, 6 and 7 - where they used 8 and 12 mp images from their phones to create billboard-sized images to extol the quality of their phones' cameras. So much for that legend.

This is the more accurate information regarding megapixels and print sizing:

http://www.photokaboom.com/photography/learn/printing/resolution/1_which_resolution_print_size_viewing_distance.htm

When you make a print from a larger sensor compared to a cropped sensor camera, you have to magnify the original image 50% more. to get to the same print size. So an 8x12 has a diagonal of 36.6 cm. A full frame sensor has a diagonal of 4.32. The magnification factor of a full frame sensor to get to that 8x12 print, assuming no cropping, is roughly 8.5x. But an APS-C sensor with a 1.5 crop factor has a diagonal of 2.82, so to get to that 8x12 you have to magnify the image 13x. Along with that you magnify focus softness, chromatic aberrations, noise, and other image flaws by 50% over the larger sensor. The end result is that all things being equal, which they are not, the crop sensor camera cannot produce the same level of image quality. No one seems to understand this.

Another urban legend is the matter of increased "reach" when you use a crop camera. when you compare the output from an 11.5 mp image from a D800 (in DX mode) to the same image using a 12 mp DX camera like a D300, using the same lens with the image centered in the viewfinder, you will be hard pressed to tell the difference. This is not a great comparison since there are some "generational" differences where sensor and processor technology is older and noisier in the D300, but assuming decent light, there will be nothing that would make one any better than the other.

If you compare a 20 or 24 mp APS-C camera then the detail capture is likely better due to the smaller pixels and greater pixel density, but the noise will be worse. I shoot birds and wildlife, and image quality on a D800 is noticeably superior to any crop camera, and I've tried the D500 and D7200. Not a fan of either. They are great cameras, but not for the way I use a camera.

I would rather have a 36mp full frame sensor when using a 600mm lens where the subject is less likely to fill the frame, than a very tight composition with the same lens on a crop sensor, with little to no margin of error.

Main advantage of full frame - better image quality, especially when printed or projected. If discussing high mp cameras then a greater ability to crop and still maintain image quality when using sharp lenses. If looking at low mp cameras like a D3S or D700 at 12 mp, the giant pixels provide exceptionally good light gathering and even though these are old cameras, they still provide outstanding high ISO, low light performance, compared to current cameras. Lenses for full frame cameras cost more, but are usually better in build quality, sharpness, color rendition, light transmission, dust and moisture sealing etc - worth every penny. Full frame camera bodies tend to be bigger, and if you have large hands, they will feel more comfortable.

Oh, and one last thing - crop sensor cameras, using the same lens at the same distance, will have LESS depth of field than full frame cameras. The full frame camera will have roughly 50% greater DoF, front to back. What befuddles everyone is that the comparison where crop cameras are believed to have more DoF is not made with the same focal length at the same distance, but rather the same "composition" or size of the subject in the frame, which necessitates the camera being moved back from the subject which in turn results in greater DoF when using a crop camera. If you have any doubts, consult your favorite online DoF caculator.

http://www.dofmaster.com/dofjs.html
http://www.cambridgeincolour.com/tutorials/dof-calculator.htm
http://www.outsight.com/hyperfocal.html
http://www.photopills.com/calculators/dof
http://www.tawbaware.com/maxlyons/calc.htm

They are all consistent.

The disadvantages of full frame are not related to image quality - full frame cameras and lenses and filters are usually bigger and heavier and more expensive, and they are often noisier. They can be more intrusive in certain situations when a small quiet camera is an advantage.

And Zach Arias is a funny guy, for sure.

The same discussion was brought up when Olympus Yashica (they had the Samurai DSLR), Rollie 35, Alpa and other camera mfgrs made half-frame cameras in the 50s and 60s - they had lower image quality, and as a result, were not taken very seriously by the professional community.