I have a Canon Rebel XTi and some decent lenses. I am considering getting a 500-1000mm f/8 telephoto zoom lens.
For photographing birds that are 25-100m away, should I use an automatic focus or a manual focus lens?
With a Canon Rebel XTi and a 500mm - 1000mm f/8 lens, the question isn't really, Should I use Autofocus or Manual Focus but more so Will Autofocus Work At All?
The Rebel series is a consumer grade series - it was never designed for tracking birds in flight, for example.
You've got 9 focus points and, for the life of me, I can't remember or find in the manual what aperture is required to run them. This question has a wealth of knowledge on the subject though: What apertures are required to enable autofocus, including cross-type or high-precision focusing, on Canon DSLR cameras?
To put it bluntly, with an f/8 lens, I'm not sure if any AF point except the center will work for you at all. Perhaps on a very bright day, but I wouldn't expect much from it during golden hours.
At best, you'll have some limited AF functionality or center point only functionality. At worst, you won't have AF at all and will have to manually focus.
If your subject isn't moving, I'd try using AF first and then go with manual. The problem with manually focusing with a modern day SLR/DSLR is that they don't expect you to - there are no focusing aids built into the camera (like a split screen/microprism). Some newer cameras offer Live View, which may help you out - it won't do well for birds in flight but stationary ones may work out.
For birds in flight, the same holds true - try using the center AF point and AI Servo to track...but realize that you are asking a lot from your camera here...keepers may be few and far between.
Two things that make the question moot:
For more on the whole "aperture limited" thing with regard to autofocus, you can read this answer to Comparing Canon EF 100-400mm f/4.5-5.6L IS II USM and Canon 70-300mm 1:4-5.6 IS II USM with Kenko 1.4x MC4 DGX
There is a difference between being rated to focus at f/5.6 as most of the older Canon cameras are and being firmware limited to f/5.6 like some of the newer Canon cameras are. Older Canon cameras rated to focus with f/5.6 or wider lenses will sometimes focus at f/8 depending on conditions. But that ability will be fairly limited to very bright light and will be excruciatingly slow, especially with cropped APS-C cameras. I once tried it with a Canon EOS 7D + Kenko C-AF 2X Teleplus Pro 300 DGX + EF 24-105mm f/4 L IS. The only thing it would AF on, and then only some of the time, was a bare light bulb using the center AF point.
For birds at rest, you can probably get away with manual focus. For birds in motion/flight, you would have to be very good with your manual focus to be successful. Autofocus would have a much better chance in that case, and preferably one of the tracking autofocus modes if your camera has it (e.g. Canon's AI Servo mode or the equivalent for whatever manufacturer is appropriate).
You are going to use manual focus, because on these cameras the AF is not functional past f/6.3 (which is why the big 150-600m zooms from Tamron/Sigma are f/6.3 at the long end). Still true on my 70D which is several generations younger and one market band higher.
With a 1000mm lens your depth-of-field is quite shallow. On this online computer:
Subject distance 50 m
Depth of field
Near limit 49.6 m
Far limit 50.4 m
Total 0.74 m
In front of subject 0.37 m (50%)
Behind subject 0.38 m (50%)
Hyperfocal distance 6579.9 m
Circle of confusion 0.019 mm
This means that you can't set your lens to some focus distance and shoot without focusing.. you are not too likely to catch sparrows in flight. You can at best get sitting birds or gliding seagulls.
Don't get too hooked on focal length. Before shooting a bird you have to see it, so the longer your lens, the better your eyesight.
You lens is likely not stabilized. So at 1000mm on a crop-sensor camera, you have to shoot at 1/1500s. Compound that with the f/8 aperture and a fairly old sensor that has a low ISO sensivity, you will need a lot of light, even an overcast sky will be a problem.
As I said before, a $20 a ghillie suit will get you closer to the birds than a $2000 lens.