Take Cover either drops your shield where your standing, or rolls you into cover (if you are facing one of those green siloutettes). Crouch just drops your shield where your standing.
If you use Crouch behind cover, you will still get the benefit from being behind cover.
The main reason i switched to Crouch was because Take Cover kept making me roll into cover too close to enemies, causing them to aggro on me. IMO Crouch is just more reliable.
Just have both, look if there's a green body somewhere and if there is hit the other keybind. Personally I have Take Cover(The one that rolls) on F, and the one that crouches in place on Alt+F.