At what level does analog beat digital?

At all levels. Most of the people out there really don't have the software library or the gear to compare the two formats, nor do they intuitively understand the value of analog. They want accurate and easy, not musical. Maybe they think tubes are a dumb and outdated idea too? If you're a music lover, you go to the trouble, expense, and time to listen to music.

I prefer to not think in terms of better... I would say Cd is better if I want something easy and fast, multi hours of non stop music...
LP is more labor intensive, needs more involvement,(and LP playback is rewarding in being ultimately more satisfying for that effort.) and is equally as interesting, in a different way, than CD.
IF the pre, amp and speakers are the same, and it is just switching from one source to the other... IMHO one would spend about the same on the analogue portion of the system as on the digital... in a mid-fi* system (*$3,000 to $10,000. total all stuff)
In a low-fi system ($300 to $2,000 it all depends on the kind of flaws you prefer...)

I will compare Audio aero capitole mkII with the Nottingham Hyperspace table /anna arm/benz ruby II. I listen to cd's a lot more because its easy and there is more new material than vinyl. That said the resolution and detail is still better with well recorded vinyl. It did cost a lot more for the analog side because you also need a exceptional phono stage. I use the Manley steelhead.

Ozfly, will the Teres be good enough? Just asking. I just purchased a used Dennensean air suspension and granite slab for my creature on steroids and is amazing how vibration can rob the system of clarity, musicality and imaging. Once the creature was placed on Goldmund cones and cork underneath the soundstage expaned outside the speakers in a full manner. I can see that an analog rig would have to be pretty stable and clean in order to bring that out...

Psychicanimal, I would love to get a Teres someday. I honestly believe a superb analog rig would be great in my system. But, $4,000 - 6,000 for the turntable, $3,000 for the tonearm, add the cartridge, add a great phono preamp and you are in the range I discussed above. My company did very well this year. If all goes well, I might just do some shopping in March. I will certainly check the threads here and ask for advice. Someday, I will have both an excellent analog and digital front end. Then, let the tweaks continue ;-)