New LP's made from analog or digital masters

To directly answer your question, most new LPs are made from digital masters. I'm talking specifically about new releases. Not new vinyl releases of old material.

In most cases, the vinyl will still sound better because the digital masters are likely hi-rez digital. To produce CDs, the hi-rez digital must be down-converted to 16bit/44.1khz which is where the big loss of fidelity occurs. This process obviously doesn't occur when mastering for vinyl. (Or I should say it SHOULDN'T occur... Remember the Norah Jones album whose SACD and Vinyl versions were cut from the 16/44.1 CD master? Oops.)

Cheers.

Mapman,
You are correct that we vinyl enthusiasts are a little harsh on CD. It's payback for CD being so harsh on our ears for 20 years, I guess.
I think I never forgave the record industry for forcing CD down our ears and having the nerve to tell us it was "perfect sound forever" when, in fact, the sound was awful and CDs scratch just as easy (if not easier) than records.
CD quality has improved markedly since 1982. Some LP's that I buy contain a the CD of that recording. In many cases, the difference between LP and CD is quite small. Usually the difference is most apparent in the bass. With bass, the CD will have "thwack" and the record will have "thump". Many will prefer the "thwack" as it is more exciting and attention-getting, but "thump" is really closer to what that instrument sounds like.
On "Together Through Life" by Bob Dylan, I compared the LP and CD. Very close, but while the bass sounds good on CD, on vinyl it's extremely obvious that a large, wood-bodied instrument is being played.

Cheers.