I have an AE-1 and a recently-acquired F-1N (with AE finder). If the battery fails on the F-1 -- I use a Silver Oxide 6V, same size as AE-1 battery -- the mechanical shutter speeds are 1/2000 to 1/125 sec., "S" (1/90 sec.), and "B" (bulb). I haven't had battery failure, yet, as I check my battery before going out, and usually carry a spare.
I've had the AE-1 since about 1978; still works perfectly. However, I now use the F-1, almost exclusively; it's a great, solid camera. I bought mine through KEH (http://www.keh.com/).
The above post finds another good resource. I've never used the EF, but have heard nothing but very good things about them.
The following site holds an archive of information/descriptions on the entire FD line-up, with links on each page to other dedicated products, including cameras, lenses, and accessories. I hope you find it useful: