Digital cinema is kinda a double edged sword. The screen door effect is pretty aparent on the digital projectors they use when doing the garbage ad's before movies at AMC theatres. I suspect they are using 2K DLP projectors though. (2048x1080 pixels). 4K projectors would likely be very good for digital cinema, so if they have those, the screen door effect will be very muted, and I suspect this would allow for a very good movie experience. 4K has 4 times more pixels than 2K.
Recently I read about a company that created an 8K projector, or at least source video that was in 8K format. Turns out the projector is actually 4 4K projectors digitally combined to create one giant 8196x4160 resolution movie.
The reason for the switch to digital cinema, is that it can cost ALOT of money to send out a film reel to every screen that is planning on showing a movie. The reels themself are incredibly expensive simply to produce. However with digital cinema, as long as the source server has a big enough data array, studios could theoretically stream the video to the movie theatre one time, and that theatre would have the movie availible on as many screens as it chooses.