The 7D will definitly focus better and faster than the 550D, plus it has AFMA to allow you to callibrate your lenses... which gives more accurate focus and more keepers.
The FF cameras will outperform the 7D for IQ, but keep in mind that it is at high ISO numbers where the difference becomes most noticeable. If you are shooting in good light and below ISO 800-1600 you will probably not be able to tell the difference without pixel peeping. In poor light it a different story and FF's advantages become blatently obvious.
A big advantage of crop over FF is pixels on the subject. Say you had a FF camera and 400 lens.... If your shot had 600 pixels on the bird, a crop sensor like the 7D would give you 1000 pixels on the bird. Yes, each of the FF pixels would be sharper than each of the crop pixels, but the greater number of crop pixels MIGHT result in more detail on the final image.... This assumes that you are shooting in the "sweet range" of the 7D..... go to too high of an ISO and this no longer applies.
You could get the same number of pixels on the subject with different lenses.... a 5Dii or 5Diii with a 600 lens would be an equivalent number of pixels on target as a 7D and 400 lens, but at a much higher price... and the image would also be of a higher quality. And a tripod may have more impact than a new camera body.
In short... no easy answer..... depends on how you shoot and your lighting conditions and how much you can afford and how much weight you want to carry.
BTW, like your Cardinal picture. I don't think you will improve very much on that with a 7D.... nice shot!