Vinyl?

Just bought the new Richard Thompson album on vinyl…2 discs at 45rpm…great sounding stuff (Barnes&Noble!). 

^^^ True enough, and it also depends on the quality of the DAC between the digital file and the cutter.

Quite often my digital-sourced LPs sound better than the CD version on my home system because the DAC London or EMI used to cut the master is way better than what's inside my CD player.

Still, I hear a kind of edge to the 44.1Khz mastered Beatles albums that I don't hear on some of the classical ones (Angel, EMI) from the same label.

^^ We've mastered some LPs from source files that were 16/44 and had good results. The issue here has more to do with how the digital file was created, and it sounds like the REM LP you refer to used the same master for the LP as was used for the CD. Generally speaking, the CD master will contain more compression than the master for the LP, as it is expected that the CD will be played in a car, where there is no such expectation for the LP! But I do agree with you the production has everything to do with it!!

A bad-sounding record can also come from bad mastering--too much compression, rolled-off bass, etc.

If the original recording was 16/44.1 digital on a home computer, you're not likely to get good sound from it. I have a 2007 REM album that was pressed as two 45rpm 12" LPs. The form factor is just like a cost-no-object audiophile pressing, but it sounds like it comes from a low-res digital recording.

In general my experience matches wlutke's--as I improved my turntable damping, cartridge quality, and downstream electronics (esp. the phono stage), I got more enjoyment out of far more of my records than before.

The recording means a lot.  On the other hand, I have been pleasantly surprised by some recordings I thought were bad, only to find them excellent once my system was brought up to a level that could handle all the information presented. 

You may be right, it's subjective. I can't really be absolutely sure because my analog rig is better than digital, but still I have an impression that every recording I have, even a very poor one, done in analog sounds better on vinyl than on cd, often much better. What's more, digital recordings or/and mastering also sound better on vinyl, at least Japanese vinyl. They sound digital, just better digital.
Is it worth, say, paying $150-$200 for an original edition of Pink Floyd album in NM condition compared to $30-$40 for digital disc? It would be for me, though in this example I am okay with $50 Japanese release.