Having shot all three (I own a National Match M-1, a NM M1A (the civilian (non-auto) variant of the M-14) and "more than one" AR-15), I can tell you that I vastly prefer the M1A.
The only time I ever had the M-1 'jam' was when it suffered a round of .308 through it during a match, resulting in an 'X', but also a failure to extract. I signaled a malfunction, the armorer came over, checked with me (3X) that the round had gone downrange, then placed the butt of the rifle against the ground, and stomped on the operating handle with his boot. The rifle extracted the (now fire-formed straight (no neck) .308 brass, and chambered a new round.
I was allowed to finish my string.
I've never had the M1A jam, but it probably only has 10,000 rounds through it (and yes, it was new when my father (who used to shoot classified as 'Distinguished') purchased it in the early 60s.)
The AR15s, (Colts, all) are, by any comparison, toys.
These days I shoot a Model 70 Winchester in .308 (it and the Garand were both my grandfather's.)
Since this is HN:
the M-14/M1A is like Lisp, elegant, but accessible only to a few.
the M1 Garand is like 'C', everybody's ancestors used one, but few know how to use it.
The M-16/AR15 is like Perl, cheap, but prone to failure.
The AK-47 is like PHP. Even the retards can make one work.