When does analog compete with digital?

I agree with those who say your question is backwards. Yes, digital can be very clear and extremely detailed. However, this is at great expense in other areas that many of us consider much more important, such as more correct reproduction of instrumental and vocal timbres. Another big difference is that the distortions inherent in the digital realm, even though they are much less than in analog, take place at higher and much more musically objectionable frequencies. Digital processing also simply removes too much information, IMO. The designers justify this by saying that the human ear cannot hear most of the info they are removing, yet research has proven that the brain can still perceive frequencies above what the ear can hear, for example. There is also in digital too much loss of what is sometimes called "low level detail," one example being ambient noise in the concert hall that an orchestral recording was made in, which of course contributes greatly to the effect of the music.

All of these examples above apply much more to acoustic music than electronic, however. If you listen to mostly electronically produced music, then these things probably won't bother you nearly as much as they do others. It's a question of what your priorities are, and only you can really determine that.

Syntax,
You need a PS-X9 with the remote. I finally found one for mine.

Naim gear has long been known for its ability to reproduce music with its original rhythm, energy, and forward momentum intact. Some analog gear (Linn, Rega, Roksan) is also known for this quality. When you said you "still feel like something is missing" when listening to your analog source, my conjecture is that your phono stage, and possibly your turntable/cartridge combination, is lagging in that area. I don't know what dealerships and product lines are available to you locally to audition, but the Dynavector P75 I suggested is widely marketed and is a product that does not mess up the temporal qualities of music. Same with the P3-24, which is most often paired with Rega's own Elys 2 cartridge or with the DV 10X5. I don't know that this is the missing factor for you, of course; it's just my best guess.

...when it comes to more complex music, I much prefer the analytical sound of digital, which is more clear and 'in your face', so to speak.

FWIW, the opposite is true in my system. On music of any complexity, regardless of genre, my vinyl setup challenges the clarity of my digital, exceeds it in presence (if that's what "in your face" means) and demolishes it in terms of low level detail, micro-dynamics and harmonic complexity.

My system differs from yours, obviously. My pretty decent digital player retails for just $2K (+ another $2K for interconnects). My vinyl front end retails for over $20K.

Why this particular ratio? Why not a $20K digital source and a $2-4K vinyl one? Because IME my ratio provides better sound for the money.

No digital front end I've heard - at any price - can approach a really good vinyl rig. IMO this is because the two systems are flawed in fundamentally different ways.

Most vinyl flaws are generated during playback, which means they can be reduced by user involvement (better setup, better gear). OTOH, many digital flaws are inherent in the medium and cannot be reduced by the user for any price.

Further, with vinyl the performance ceiling has not yet been reached. No vinyl replay system in existence is capable of extracting all the information in an LP groove. Despite my seemingly crazy ratio, there are upgrades that would take my vinyl rig's performance even higher. Analog sources contain enough musical information to allow changes in even a high end playback system to make real improvements.

So, as others have said, the better question would be, "When does digital compete with analog?" IME the answer is, "When the analog playback system is of a low enough level so that its (avoidable) flaws outweigh the (unavoidable) flaws built into existing digital media."

PTM hit it on the nose with the multiple components fact of life in analog. I think we all have a price threshold that we psychologically are willing to spend on a component. With analog, over time, we can get up to that level on multiple items cartridges, tables, arms, phono stages, and cleaning. Before you know it, you have a considerable investment because it is in pieces.