The advantage of mirrors over prism to perform this task is cost. Mirrors are cheaper than prisms. If you look at camera, Single Lens Reflex-types (SLR), you will notice the bump on top that looks like a peak. Inside the camera, placed between the sensor and the lens, you will find a mirror that is mounted at 45 degrees. When this mirror is down, it reflects the image from the lens upward toward the element that will flip the image around and present it right side up with the proper left and right to the eyepiece. This element is either a pentamirror (cheap) or pentaprism (more expensive.)

It's the same principle for the device being discussed in this tread. The cheap one is made with mirrors and the more expensive one is made with a prism.

To answer sigfreund's excellent question, I dread having to put such a device in front of my superb riflescope. Yuck.

March came up with a different solution for ELR with the introduction a couple years back of the Genesis riflescope. This riflescope uses the very best optics frozen in a main tube that is adjusted externally. The March Genesis 6-60X56 has a wide angle eyepiece and has 400MOA (114MIL) of adjustment range; 350MOA (100MIL) up and 50MOA (14MIL) down. It also has 75MOA (20MIL) of left and right adjustment.

Because of the external adjustments, you get the best view through the scope regardless of elevation adjustment.

You can read about it here:
https://marchscopes.com/scopes/d60v56gfml/

There is a smaller version, a 4-40X52 WA. Both use the High Master lens system.

The March Genesis is an excellent scope but does present the issue of changing the scope cant and therefore raising the ocular and lowering the objective when increasing the elevation; this requires you to change your position on the rifle either on the cheek rest or butt pad in the shoulder or both. Of course this depends on the shooter and how much elevation he dials. Another issue when shooting at very EXTREME distances is the amount of scope cant and the length of the barrel. It's possible to have barrel shadow in the scope if you're running a long barrel and significant scope cant. While this can happen with the add-on systems as well, tacomHQ has the Delta TARAC which is mounted on the side so cant of the scope/barrel shadow is a non-issues.

There are a few adjustable bases out there; Ivey, Cold Shot and ERA-TAC just to name the most common. I use the adjustable scope base/ring set-up made by ERA-TAC which mounts to my 30 MOA integrated scope rail and allows me 0-70 MOA of additional cant. While the March is convenient and allows adjustment on the fly, you still have to/should make adjustments to your position on the rifle when using any system that changes the scope's cant.