I’ve never really played with either of these. I did use ObjectID some (considerable) time ago in a single specific project, though the need was made redundant with Blender developments, and so I haven’t used it since.
Now, I have a scene where, in compositing, I desaturate the final render a little, though I had a single texture that I did not want desaturated. Enter Material ID. Does the job a treat.
How does this stuff not get more attention?