When does analog compete with digital?

They are different. Period. If you want the equal of your digital, in a vinyl system, it is NOT gonna happen. If you want a different, but equally exciting sound, then it DEPENDS on what you listen FOR, in the sound, as to how much it's gonna cost you to get there.
I have both digital and LP. My digital is cheaper than my TTs. But i use a tube buffer to tame the digital. The Lps sound clearer, better, but the CD is more convenient.
I just have to say again, it is a DIFFERENT sound. If you are ready for it, then you could be happy. If you want it to be like your digital, you are in for a bummer.

The problem is the cost of getting even reasonably decent analogue components (yes, plural) just has to exceed the cost of getting decent digital. Lets face it, you can get very good digital for less that $1000, and actually can get reasonably good digital for less than $500. All this at new component retail prices.

For analogue you need a turntable and arm, a cartridge and a phono stage. That's 3 components that need to work synergistically. Even if each one is bought used you are still talking bottom of the ladder components for somewhere in the $1000 ballpark. Of course setup is still a very key component of making vinyl sound great.

The real value in my mind is that significantly better digital than, say an Oppo, isn't gonna cost all that much more. You cag get near state of the art digital for $2000-3000 these days. With vinyl it just keeps getting better as you decide to move up the ladder. It really doesn't top out as fast as digital, which means you can certianly spend far more, and that you will constntly feel that ypou can make it better if you just upgrade here, then here, then here ...

Disagree with Ptmconsulting about 'resonable' digital. Mostly it goes to what sound one desires. Digital has it's own flaws that no $500 or $1,000 is going to come near fixing if that stuff bothers you. if the digital sonic flaws don't bother, then it doesn't. Same for analog. A cheap TT and cart with a cheap phono, say $500. IS going to sound JUST AS GOOD (with different flaws) as that $500 digital front end. They will have different sounds, different problems with the sound, but, IMO, will really be just as good as each other.
I think the issue is: What is your preferred poison?

Bad idea trying to equate one with the other. They are inherently different Better to shoot for a single particular sound you like and tune each t that separately over time until achieved. For most, if done right, it does not have to cost a fortune.