With the used price of the MkII these days it's a tough call unless your budget dictates the choice for you,..
MkII Vs. MkIII AF:
Between the two IMHO it's a practical wash..
The MkIII had many supposed AF improvements engineered into it,. however at launch and for over a year thereafter it was plagued with issues that prevented it taking the AF crown from the MkII.
After over a year of dealing with this and finally getting a replacement camera from Canon, I find though my new MkIII AF is at long last is excellent, however I can find no concrete evidence that it is in fact any better for Birding than the MkII. Easily Just as good, but not in a league of it's own.
MkII Vs. MkIIIfor high ISO noise handling:
This is a different story. If you need to shoot low light or simply high ISO for faster shutters, the MkIII is a significant improvement on the mkII.
Further, image quality and color are simply better all around.
One can happily shoot ISO 800 on the MKIII and compare that to ISO 400 or lower files fro the MkII. Further, the higher ISO MkIII files up to 1600 clean up amazingly well with a good NR software plugin.. resulting in images that look like they were taken again t ISO 400 or so on a mkII.
Again the overall IQ is simply stunning.
Ergonomics and Control:
The MkIII again wins in a colossal lead. Going all the way back to Canon first consumer DSLR, the D30 3MP, and there first Pro DSLR, the 1D 4.5MP, Canon was using two entirely different menu systems and control layout. While the D30 evolved to the D60, 10D and 20D, Canon made substantial improvements in the intuitive nature of the menu system. Meanwhile the MkII and MkIIn came out with virtually no change from the menu structure of the the original 1D, in fact, the 1D borrowed it;s own digital menu system from the earlier Eos 1V film systems,. to make the switch for pros from the 35mm to Digital "easier"
What this results in is an archaic menu structure, that is cumbersome and time consuming to use.
Consumer lever 10D-50D menu system = excellent,
1D-1D MkIIn.. = not so good
With the MkIII Canon combined the best of each and made it even better.
In use the MkIII is a huge improvement. Here the MkIII hits it out of the park.
Given the cost of a used MkII, it's hard to make this decision. You are guaranteed one of the fastest focusing cameras ever made, with the longest and best track record for fast action birds, sports etc. at rock bottom price.
MkIII adds to that the negative of flaky AF on some bodies, along with the better IQ and far better ease of use.
Hope this all helps.