the only differences between the Mk II/III and 22/45 are:
22/45 has a 1911 grip angle and a 1911 style mag release
Mk II/III has a much more raked grip angle, like a Luger, and heel type mag release
In MA, it's easy to find a Mk II/III with replaceable grip panels, but hard to find a 22/45 with them
The Mk II/III has a metal frame, the 22/45 has a plastic frame.
For a target gun, it really matters what your body geometry is. Some people hate hate hate the raked Mk x angle, some people never really shoot the 1911 grip angle correctly.
Newer versions of each are drilled and tapped for a scope rail.
You can get a Mk x with non-adjustable sights, I've never seen a 22/45 with fixed sights or a skinny barrel.
If I were you, I'd try both out before buying. At least do the "close your eyes, point at something, open your eyes, and see how far off it is" test with both. One of them will be way off, one will be much better. You can do that in a shop.