A FF camera has a larger area, BUT...
Has shallower depth of field (NOT always a good thing, ESPECIALLY with long lenses)
This is a misconception. FF does not have shallower DOF. It only has the option for less DOF when needed.
Sure it has shallower depth of field 50mm at f4 on a 7D is roughly equivalent to 30mm f2.5 on a 5D. Same framing, shallower depth of field. When shooting birds in flight, I need usually f8 on a 7D to get the bird at least mostly in focus. On full frame? That's f13. To maintain shutter speed, that means ever rising ISO's.
Yes. The Hi ISO advantage disappears.
And that is just plain BS you are talking. Assuming that you are taking a photograph of a bird with a 400mm lens 50 feet away. Let's see how the DOF works out at f/8 with the 5D3 and the 7D -
7D: Total DOF is 1.41 feet
5D3: Total DOF is 2.23 feet
I think that there are circles of confusion here! It seems pretty obvious that if you have the same lens it gives the same size image on crop and FF sensors, and if the two images are viewed at the same size on a screen or print they will have exactly the same depth of field. If they are not enlarged, but the FF is viewed at a smaller size, it will only appear to have a greater depth of field.
The arithmetic from the DOF calculator proves that the images have the same depth of field when viewed at the same size. The depth of field is calculated from the size of the circle of confusion. For the 5DIII it is 0.03 mm, for the 1.6x crop 7D it is 0.019. And 0.03/0.019 = 1.6. So, when you enlarge the FF image 1.6x to get the same size image as the crop, you exactly compensate for the difference in circles of confusion.
Similarly, look at the ratios of total DOF of the 5D3 to 7D. It equals 2.23/1.41 = 1.6. The image from FF has to be enlarged 1.6x to give the same size print as the crop, and in doing so you multiply the out of focus regions 1.6x and so reduce the depth of field 1.6x.
If talking in terms of equivalence, yes.