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.

Try not to worry about such things. Establish a realistic budget for analogue. Investigate, read reviews and search forums on personal opinions and advice. BUT! be very careful entrusting completely in what others from so called experts and those who are not may say. Gather a list of products that fit inside your budget. Study each and try to weed out the chaff from the wheat so to speak. Then you will be able to make better buying decisions. Once you then buy and carefully set up the analogue products you need, JUST ENJOY!

In time as your future tastes and budget evolve you can as per this hobby swap out other gear if you wish.

You can get great analogue playback if you are wise with buying for even under $1,000 total purchase, new or used turntable, cartridge and phono preamp. Even at this it may provide you enjoyable analogue playback that could have your CD player collecting some dust. That said I learned a few years ago to move away from being anti-digital. I got tired of the crap many say about it on audio forums. Even though most of the time my analogue records sound better or best to me I have a nice and still very modest digital setup, basically now a Oppo BDP-83 and have enjoyed playing well produced CD's too. It is just that too many CD's made over the last 10+ years suck in terms of mastering and production quality. But don't think every vinyl record you buy was well mastered and produced either, some SUCK BIG TIME TOO!