I know that I've seen it somewhere else, but I'm not seeing it in the the Select By Location tool or the Spatial Join Tool.
For the Relationship in the Select by Location Tool and Match Option for Spatial Join, I would like to see something that makes sure that the center of the feature is within the boundary of said feature. Right now there is no good way to accurately select all of the features that are within, but also cross the boundary of the Selecting Features.
For example, This is the result of "Have their center in" where you can see a feature selected that isn't in the Selecting Features where the red arrows are pointing to features that should have been selected.

And this is what happens when I use Within
