I'm glad to see this topic arise as it is of major concern to me.
As a photographer who has only ever shot slide film, exclusively, this is the one reason why I have not yet switched to digital.
I could rant for a while, but the bottom line here is that a photographic type projector for digital has yet to be invented.
The present type were born of a need for executives in brightly lit board rooms and other business type functions, to show their profit line graphs. They perform that duty very well. Oh yes, they are bright, too bright. They are big too, too big (projected image I mean). Finesse?, sorry, no. Fidelity?, sorry, no. Personal opinions I may add. But I have yet to see one for the pure purpose of photographic image projection that comes anywhere near the fidelity of the projected slide film image. If bigger is better for you, then by all means....
However the previous answers posted here are all true too.
Contrast IS the biggest problem, born of too much light for the average living room. There are many sides to this topic, and I would like to see more effort by the manufacturers to address it, but I doubt it will happen soon if ever. Not enough money in it I feel. There are a couple of brands that have, in their menu's, selections for "Data", "Home Theater" and "Photographic" settings, and I noted that the "Photo" setting was actually dimmer, by default. But the attempt at correction, I feel, is feeble.
I actually asked Michael about this (subject) a short while ago, refering to what I like to call the "back end of photography" and even he agrees, saying "if projection is your thing, stick with film".
Digital for prints, I believe, is now King, getting better all the time. Slide projection will probably remain the last stronghold of film for the foreseeable future at least.
DK