Keep in mind that crop factor does NOT give you more reach in itself, your 400mm lens will project exactly the same size image on the sensor regardless of whether that sensor is a FF or crop. The 1.6x comparison is simply to compare the focal length difference required to frame the subject the same way between different formats. The projected image is the same size, but the crop sensor doesn't record as much of it, if you take a shot from a FF sensor and crop it to the same field of view you would have recorded on a crop sensor they will have the same image. So you can get the same "640mm" lens on the FF by simply cropping the image.
As you are generally going to be cropping most bird shots anyway, regardless of FF or crop sensor, then the "1.6x" figure is useless. If you crop the image (from a crop sensor) to the framing you want of the bird, it is exactly the same as cropping from a FF sensor except you throw less away. The sensor area used for your final image is the same, whatever the size of the actual sensor. So, the images have an identical crop factor of maybe 2x or 2.5x compared to a whole FF sensor. This makes your lens an "800mm" or a "1,000mm", except of course, it doesn't change the lens any more than using a smaller sensor. The lens is always 400mm and whether you crop by using a smaller sensor, or cropping the image from a larger sensor, there is no more "reach".
Where you CAN get more "reach" is with pixel density, and crop cameras typically have more pixel density than FF ones. The 7D mkII has almost as many pixels as the 5D mkIII, but in a much smaller area. This gives a lot more "pixels on target" and, when you take your cropped image from each camera (using the same amount of sensor area) the file from the 7DII may be 2500 pixels wide but the file from the 5DIII may only be 2000 pixels wide (I haven't done the math, so nobody jump on me for not being exact here, I am just pointing out the principle). Hence the 7DII image will be bigger, therefore has "more reach". That difference though is not related to the crop factor of 1.6x, it will probably be less but depends very much on which cameras you compare. A high megapixel FF camera, such as the Nikon D810, could have higher pixel density (more reach) than an older, lower megapixel, crop camera.
So, yes, you are going to get more reach from a modern crop body than a FF one (if you are sticking to Canon) but from pixel density, not crop factor, and forget the 1.6x figure as that means nothing where "reach" is concerned.
I always used to use my crop bodies (20D then 40D) for bird photography in preference to my FF (original 5D) however since I bought the 5D mkIII that has become my primary bird camera, and it does a damn good job at it too. However, if birds are your main subject, I would suggest the 7DmkII as you will get significantly more pixels on target. The 7DII is on my shopping list for next year, to replace the 40D, and I will then use that for bird photography in preference to the 5D mkIII.
+ 1 + 1 ... this is probably one of the best descriptions of FF vs CF in non-technical statements that I've ever read on here. Take a good look at this, and try to understand it in terms of what it does to the image as it relates to the distance from target.
Only thing I'd add, newer cameras have better technology, therefore, using a 7D will give you "more data" per mm of sensor than older FF cameras. So, it's not always a direct comparison in the sense of that 1.6 CF multiplier -- that really relates more to what you see in the viewfinder than it does actual "magnification" of the target ... the target "appears" closer because the lens makes the frame smaller -- sorta