Not sure what camera you use, but if you shoot a high-res FX camera, you can "zoom" a little by cropping.
(I'm guessing with small birds you usually want to zoom
in rather than
out 
)
A couple more of points on the 200-500 vs 500PF:
The 200-500 focuses to 2.2m, giving 1:4.5 magnification, the 500PF focuses to 3m giving 1:5.5 magnification. Both focus pretty close for this focal length but the zoom obviously does better here. I guess you are usually shooting at much greater distances so this may not be very relevant.
The 500PF is slightly shorter than the zoom @200mm, and significantly shorter than the zoom @500mm, so should be easier to transport and more agile in the field. It's also only 2/3 the weight although if you shoot from a tripod that may not be much of an issue.
All the best with your decision!