Control Grips in Families

I'm referring to the little control arrows you see in some content.

Revit offers us four versions

Single Vertical - "rotates" the family over the origin of family
Single Horizontal - "rotates" the family over the origin of family

These both maintain the "handed-ness" of a family, such as a desk with a left-hand typing return. If the family is only supplied with a single orientation or shape, not a mirrored version then these two controls respect this configuration by not "mirroring" the family.

Double Vertical - "mirrors" the family over the horizontal axis (origin of family)
Double Horizontal - "mirrors" the family over the vertical axis (origin of family)

Further if you choose to the use the Space Bar to rotate a selected family (after placement) the single arrows rotate the family in 90 degree increments (by default unless they are over an element at a different angle). Using the Space Bar with families using the double arrow controls will mirror instead of rotating.

Want to watch a Video?

If you pay close attention you'll notice that the single vertical and horizontal arrows change the family in the same way so there isn't a strong reason to use one over the other unless you plan to use the Space Bar more than clicking on the controls directly.

What isn't in the video is adding both double control arrows to a family, like you see in the door in the plan view image above. That produces rotation (even for a door after placement, flips hand and then swing) using the Space Bar and provides the option to mirror the family using the controls directly. Putting both the single controls in a family doesn't provide a significant difference, still rotation only, no mirroring.