Projectors are very sharp, if you get a good one. I've seen plenty that are absolutely stunning - of course these are the $20,000 ones, so I'd expect them to be good. In fact the picture is so sharp that if you examine it close up, you can see the individual pixels perfectly defined. The only problem with these is the resolution - only 1280x1024, and the fact that it is a fixed resolution, just like LCDs - so if your computer is set to the wrong resolution, text will appear awful.
Also, I'm not quite sure why you say cinema isn't sharp - it is the sharpest moving image display system we currently have - Have you ever walked right up to a cinema screen and looked at the picture when it projected by a top-notch 35 or 70 mm film projector? The level of detail is scarcely believable.