Both are/were good cameras with the AE-1 being the more popular of the two and is considered by many to be somewhat of an iconic body.
Both were very reliable, with the Canon being the most reliable of the two.
Both use lenses that have not been manufactured for more than 20 years. So which ever one you buy, realize that you'll be buying into a completely obsolete system because both of these brands changed their lens mount in the mid 80s when they switched from manual focus to auto focusing SLRs. Two brands that didn't change mounts were Pentax and Nikon.
Choosing either one will be fine as neither provide any specific feature(s) that will increase image quality. Remember with an SLR, there is literally nothing but air between the rear element of the lens and the surface of the film. The body is nothing more than a box that hold the film and cannot have any affect on image quality. With said, the differences in SLR bodies is the level of control that each one offers over the image-making process. For example: The AE-1 can accept an auto advance drive which will advance the film 1fps. The X-700 can accept a motordrive which often allows frame rates of around 5fps. The Canon A1, which is superior to either the AE-1 or X-700, also accepted a motordrive producing 5fps. The last in the line of Canon's manual focusing SLRs was the legendary T-90. This body was designed by Porsche and was a precursor to the EOS system. IMHO, the T-90 was the best and most advanced manual-focusing SLR ever made. It was one of the first SLRs to have a motordrive built into the body. Disclaimer: I used to own one back in the late 80s. I eventually sold it used for more than what I had paid for it new which should tell you a lot about the quality of the camera.
If you want a manually focusing SLR and would like to be able to use those lenses on a modern DSLR, then look at either Pentax or Nikon. Pentax's K-1000, ME, ME-Super and their professional LX are all great choices, especially if you want a small form factor. Nikon's FE, FE2, FM, FM2, F3 are also all great choices. Stay away from the Nikon EM which was full auto only and is considered one of the worst SLRs Nikon has ever made, with the possible exception of the N4004.
If you do with an auto-focusing SLR, then you'll be able to use those lenses on any modern SLR. Any of the Canon EOS SLRs are great especially the A2, EOS-3 and EOS-1. Nikons are all good (except for the N4004) especially the N90, N90s, N6006, N8008s, and F100.
I wouldn't bother with any of the AF cameras from Pentax, not when the bodies from Canon or Nikon were so much better.
I would also avoid any of the Minolta Maxxum cameras as they had design flaws making them the least reliable camera on the market at the time.