aishiwoo

Agree with the above C hings ~

For beginners, 400mm is fair enough, RAW should be used and the photo could be chopped.
Actually, you would find that even though you have 800mm lens, it is still not long enough (the birds are as small as a seed in your image)
Thus, more importantly, you can take nice photos if you have a good position and a good understanding on their lives.

I also use 7D + 400mm f/5.6.  I am satisfied with this combination.  But my techniques in birding are required to improve.  

456 is not so general for other topics as the closer focus length is 3.5m and no image stabilizer.  If you would like to use the len for other purposes, it would be better and flexible to have 300mm f/4 + extender.  Bear in mind, the quality would be decreased by using 300mm f/4 + extender, especially the photo are chopped.

aishiwoo

I also think that image stabilizer is good and useful but not essential.
It is better to carry 456 with a tripod.
The correct pose to hold the camera and len is also important to have a good image.
I would use Tv mode to fix the shutter speed at around 1/400 - 1/600 and auto ISO.  So far, hand shaking is not a main problem.

aishiwoo

Welcome ! Right ~~ Louis, people in the past also took excellant photo without IS even without AF.

Nice !! Bob   Haha ~ for convenience reason, I seldom take tripod.  But it is a good habit to have tripod with the camera specifically in birding at a fixed point.