I completed a pair of test boxes to compare a planar tweeter to the Vifa dome as used by Wayne in the one and two Pi designs. My boxes are larger than the one Pi. At about 1.6 cu feet they are still considerably smaller than the two Pi's. So they dig just a bit deeper than the standard twos but nowhere near the towers.
And the winner is.... the good old Vifa dome. Everybody was at first impressed by the planar units, but after that initial attraction, we all thought the domes worked better. (My poor wife listened to hours of listening tests. Although not an audiophile, she is an avid music lover,and has better ears than anyone else I know.)
Okay, the domes are better. But why? I suspect the planars don't move as much air as the domes at the bottom of their frequency range. People noticed that characteristic. The domes have more impact. Second, the planars are very restricted in the vertical plane, maybe too much so. In my room they seem unable to fill the space as well. I even tried to add them as a super tweeter to a pair of single driver back loaded horns and the sound field collapsed a bit. Perhaps planar types work best where a lot of them can be used for coverage, like a home theater set up.
I also note that most of the really expensive and highly reviewed speakers eschew ribbons and planars. Some of the domes they use are quite expensive so cost isn't a factor.