The Canon A-1 arrived in 1978, two years after the AE-1, and it was the first SLR that could choose both the shutter speed and the aperture on its own. That was a serious piece of engineering at the time. It is also why people confuse the two cameras, and why the A-1 asks a bit more of whoever buys it now.
What it does that the AE-1 does not
Five modes instead of one. Program, shutter priority, aperture priority, stopped-down metering and full manual. The viewfinder readout is a red LED display rather than a swinging needle, which is easier to read in the dark and harder to read in bright sun.
Same FD lens mount, so the same large and inexpensive set of lenses fits.
The same noise
The A-1 shares the AE-1's mirror mechanism and therefore shares its one famous fault. Fire the shutter and listen: a squeal or chirp just before the click means the lubricant has dried out. It is fixable by a technician and it is a reason to pay less. It does not stop the camera working, but it does get worse.
The battery, again
A 6-volt 4LR44 or PX28. Electronically timed shutter, so no battery means no camera at all. The cell is cheap and still made. Take it out before storage.
Where it gets harder
More electronics means more that can quietly stop working. On an A-1, check each mode rather than just firing the shutter once. Set it to program, then to aperture priority, then to manual, and watch that the LED readout changes sensibly each time. A camera that works in one mode and not another is a camera with a fault somebody did not look for.
The LED display itself fades on some bodies. Look at it indoors and outdoors before you decide.
Which of the two to buy
If you want to learn how exposure works, the AE-1 is the better teacher, because it makes you choose something. If you want a camera that will hand you a usable frame while you think about the picture instead, the A-1 does that and does it well.
If you want the fewest things that can break, neither — buy a mechanical body. That is a different article.
What we check
Every A-1 that passes through Unseend is tested before it is listed: all five modes, the shutter at every speed, the meter against a known reading, the LED readout, the aperture blades, the light seals, and the noise. What we found is on the page, including anything we could not test.