Blu-ray vs HD digital?

In my experience with Directv and a Sony BD player I say the BDP is clearly superior to the Directv HD DVR. You may get different results with the Apple product I have no experience there.

is there actually a way to run HD or BR on a server? I thought that the format is still locked up.

Yup there are several ways. You can use MakeMKV or DVD FAB to rip a complete copy to hard drive. Then use Media player Classic Home Cinema or something like Power DVD. If using across a network, it would be better to use hard line Ethernet. Because the transfer speeds are very high when streaming Blu ray, a wireless network won't be fast enough to handle the bit-rate.

Add the Blu Ray player--with your current system, the audio & video (especially the audio) will be one of the really "jaw dropping" experiences you will have as you progress on your journey to "Audio / Video PhileVille":-)

Most currently offered HDTVs have a resolution of 1080p, and most also have a refresh rate that's divisible by both 60 (for the 60Hz refresh rate of video broadcasting) and 24 (for the frames-per-second rate that film is shot). That's why most LCD HDTVs have a refresh rate of 120 or 240 Hz. Plasma typically refreshes at 600 Hz.

If you have an older HDTV or one of the down-market models with a 720p engine, your TV won't even accept a 1080p signal, let alone a 24fps one. It'll accept a 1080i signal, but downconverts it to 720p.

Concerning the predominant resolution, however, assuming you have a 1080p HDTV, the only source I know of that will feed it its maximum resolution and refresh capabilities is a Blu-ray player. Over-the-air and cable HD broadcasts are 720p or 1080i. I don't know about satellite, but I suspect it's also 1080i or 720p. Apple TV HD downloads are 720p. HD Instant Watch programming from Netflix is also a max of 720p.

Only Blu-ray also offers 1080p output PLUS 24 fps (1080p/24) as well. This synchronization with the speed the film was shot at gives you better smoother motion with less judder.