That would be a cool greenhouse to be inside of. If you can keep it warm enough you could grow some pretty tall trees (banana

). I don't have any direct experience but my guess is that you may get the same amount of solar energy through a high tunnel or a normal walipini roof. But the heat loss through the high tunnel could be worse due to greater surface area.
So if you have the same glazing between the two options, the high tunnel would likely lose a fair bit more heat at night and in the winter. Unless you can find a way to insulate the North part of the high tunnel and maybe the North half of the E and W walls. You could also potentially have a reflective inner surface on the North side of the high tunnel to bounce light down that would otherwise enter the South side and exit the North side without hitting a plant. That would give you more solar gain with the high tunnel option.
You'd also have more cubic feet of air to heat/cool/ventilate under a high tunnel which could be good or bad.