In typical situations, there's not an enormous difference between them.
The biggest differences will be found in -
Low light/High ISO performance is significantly better on FF bodies.
Per pixel detail is better if the megapixel count is similar - a 20MP FF image vs a 20MP crop camera image with similar quality lenses will show an advantage to the FF image.
Larger sensor size necessitates longer focal lengths to acheive the same viewing angle. AKA you have less reach with a telephoto lens, and you have less depth of field on the FF camera. To make things roughly equivalent, multiply the aperture on the crop camera by the crop factor for what it would look similar to.
135mm f/2 on crop
135 x 1.6 = 216mm
2 * 1.6 = f/3.2
So a 135mm f/2 lens will give similar results to a 216mm f/3.2 lens on a FF camera.
500mm f/6.3 on crop ~= 800mm f/10 on full frame
500 x 1.6 = 800
6.3 * 1.6 = 10
The full frame camera will need to use a higher ISO to acheive the same shutter speed - and this also factors in to equivalency. The FF body will need to use a higher ISO, but it will result in fairly similar image quality.
If you're looking at faster glass, here's one in reverse:
50mm f/1.2 on full frame
50 * (1/1.6) = 31mm
1.2 * (1/1.6) = f/0.75
So a 50mm 1.2 on a FF camera would be like a 31mm f/0.75 on a crop camera.
FF is less important if:
Crop cameras offer enough image quality for what you're doing
You're limited by focal length. If you're limited by focal length you will need a much larger lens to get similar results from the full frame camera
You need a faster camera: right now there's no inexpensive Canon FF body with great AF/frame rate performance
FF may be a good choice if:
You're not focal length limited by what you're doing
You desire the ability to print larger or use higher ISOs
You desire the ability to control depth of field even more