My mirror preference is based on limited mobility. An old neck injury prevents turning my head quickly and easily to look behind me.
The Mirrycle feels intuitive because it's just a typical accessory mirror used on cars and trucks I'd driven for years. It's the old "Objects in mirror are closer than they appear" scenario, in exchange for a wide field of view.
If I can't see it in the Mirrycle, it's too far away to worry about. If I can see it, I know I need to pay attention because it's probably closing the gap quickly. With the wide angle Mirrycle it's difficult to estimate approach speed, so the Take A Look is better for that. But the Take A Look's field of view is too narrow for me to rely on solely.
If I still had full neck mobility I might not use a mirror at all, although I did when I was younger and in perfect health. When riding in traffic I used a mirror with an elastic strap around the back of my hand. Very useful -- just squeezing or relaxing my grip and slight wrist rotation covered most of the road behind me.