You need maybe a 3 x 7 feet area for a person to sleep on
If you have a rectangular base tent you can more easily allocate 3 x 7 foot areas for people
But, I suppose you could have two people with their feet at one triangle point
I wonder if it would be lighter? Probably a little.
When you set up a pyramid, you have to eyeball that the base is square, or two of the ridges will be slack, with tetrahedron you wouldn't have that problem. Also, if the four corners of the pyramid aren't all on the same plane, then the tent doesn't set up right, with a tetrahedron you wouldn't have that problem - sort of like a three legged stool doesn't rock.