I just did a physical comparison between the cheap-as-chips Canon AE-1 Program I picked up today (with intriguing "Access" brand lens, which I think is a badge-engineered Soligor) and my very old OM-20. I know: each is, respectively, the successor to the AE-1 and OM-10 you're looking at, but some of this may be relevant:
The OM is smaller and lighter in weight.
Both seem equally well-built in terms of precision, but I suspect the Canon edges the Olympus in durability (though that's more than somewhat difficult to tell by hand and eye).
The control layout of the Canon seems (mostly) more logical to me. However, you might note that I have a purely personal dislike for the "around the lens mount" shutter-speed ring of the Olympus (which would make the OM-10 with manual adaptor actually more congenial to me than the OM-20). The one infelicity in my personal view of the Canon is that the AE lock button on the Canon is also on the lens mount, designed for use by the left hand that (IMO) should be preserved for focusing the lens. (The Oly does AE lock with a half-press of the shutter.)
The overall finish of the Canon seems nicer, despite my Oly being better cared-for.
Other than that, they seem very much to be rather typical cameras of their time and not really that different, overall.
You might note, though, that AE on the Canon AE-1 is shutter priority only, while the OM's AE mode is aperture priority only. If you have a strong perference, that might be the decider. Also, if you want to use the camera in manual mode, and the OM-10 doesn't come with manual adaptor, then the Olympus might require additional expense.
...Mike