There is an ongoing movement for movies to be recorded in digital instead of film. If I'm watching a movie at home on a 1080p HDTV and a bluray player, could I see the difference between something originally recorded on film vs digital? Are those differences erased in the conversion to the home viewing format? Would I have I go to a theater that showed analog films to see the movie as the director intended?
The final presentation has been digitally altered and compressed. Even if it was full quality, you'd likely be unable to tell as film grain can artificially be added (or removed) and color grading can adjust for much of the differences in the way color is captured. If no editing had been done to the source, it would be pretty clear even on your home set if you knew what to look for, but after post production is done, you can make one look like the other so that it's pretty hard to tell the difference.
As far as how you are more likely to see it the way the director intended, a high quality digital theater is the best bet. While films may be shot on film some of the time and digital other times, they never go through the entire process of editing in analog (at least not for any hollywood film and not for most artsy films either.)
The first step after shooting a film reel is going to be to scan it to a digital format so that it can be used in the NLE (non-linear editing) software and whatever compositing software is being used for effects work. Since all films go through a digital process, the process of converting back to film is more a matter of convenience for theaters that lack high quality digital projection that can match the quality of the actual digital files.
It's also worth noting that theaters that do use film projection have to worry about degradation of the film which happens rapidly and results in imperfections in the playback. Digital cinema projectors have no such drawback.
The debate in the film world about digital vs cinema cameras is rather about how the light is captured. The primary difference between film and digital sensors is not how the final product looks so much as how it captures light. A digital camera is exceedingly high quality and very precise, but similar to a keyboard that can play an exact frequency of a note, it lacks the "warmth" of film. This is similar to the CD vs Vinyl debate. The film camera captures the light differently and as an analog medium has a softer and "warmer" feel that some people prefer to the "cold" and exacting nature of digital sensors.
This is only a factor for the initial capture of the image however and after that, it doesn't matter and all parties agree that having the most accurate and exact capture in the conversion to the digital world is important, just the film buffs want it to be in a high quality scan while the digital camera guys see no reason not to shoot directly to a hard drive.
For something shot in a controlled setting, you'd be hard pressed to tell the difference between top-end digital cameras and 35mm film. The usual tells would be grain vs noise and highlight handling. Resolution is not really an issue, because even the finest film negative is reduced to (at best) 4K digital as the first step in post.
Aside from the taking medium, everything you see in a movie released on blu-ray is 'digital' from that point on (Digital Intermediate (DI) is the general term). Working in digital allows easy integration of CGI and application of other effects. Film grain is removed from the camera originals on scanning, and perhaps added to generated elements to match. Also, by the time it gets to BVD it's highly compressed, which can further mask any source differences.
Even movies released on film for theaters have almost certainly been through the DI process, and printed to film only as the last step. There is nothing I'm aware of in taking or grading that can be accomplished only in film any more.
I look forward to other opinions. (-: