The type of futuristic 3D display I'm considering would be pixel-based flat surface, like today's displays. The futuristic part is that each pixel controls what color gets emitted in a number of directions.
If such a display were used to display a 3D image, then it should be like looking through a window, where different viewing angles give the appropriate aspects of the image.
Other possible applications of such a display could include display privacy by restricting the viewing angles of the sensitive parts of what's being displayed to the those of the intended viewer, and display sharing, where viewers at different viewing angles see different images.
The 3D images could come from holographic cameras or be computer generated.
Without any solid reasoning, I'll assume that each 3D pixel captures the information of N 2D pixels for an N-pixel image.
For images on the order of a million pixels, then a 3D image would have the equivalent of a trillion pixels. Such an image would probably compress roughly like, though probably quite a bit better than, a million frame video, which would be on the order of 10 hours at 30 frames per second.
For DVD resolution of 720x480, a 3D image would be roughly the size of a 3 hour video.