Can headphones ever be as good as high end stereo?

The upside of your situation is the recent incease in options of high-end headphones and amps; Stax has more competition. I tried a few at axpona and was really impressed with Audeze LCD-3. The downside is the presentation of headphones is in one's head and does not change as you move your neck. I do not think quality is going to be the issue so much as presentation. That is up to you.

You can, indeed, get great sound from a set of headphones. The experience is quite different, and I personally don't think it is worthwhile trying to chase similar imaging with phones--I accept that phones will present sound as coming from inside my head rather than imaging like speakers (crossfeed circuits, binaural recordings, headphones with drivers that are placed to mimic speakers, etc. really aren't convincing).

I have Stax 007 (Omega II, Mk.1) phones and a Blue Hawaii Special Edition amplifier/energizer. I like this premium combination a lot. I have also heard the 009 phones with this setup. The 009s have better bass, better dynamics, and a more extended top end. But, this comes at the price of sounding brighter and somewhat thinner in the midrange than the 007. Hence, there are tradeoffs and I would not declare one better than the other sonically. Both are reasonably comfortable (the 009 is heavier). The Blue Hawaii amp driving Sennheiser HE60 phones (discontinued) also sounds quite good--smoother and more natural tonal balance, but slightly duller in dynamics than the Stax phones.

For a quite different sound--much warmer, but lacking in the clarity of the Stax phones--I like the Audeze LCD-XC. This closed-back version of the Audeze planar magnetic phones is very nice sounding to me. Audeze phones with a really good amp, such as the Viva headphone amp, would make a killer system. The Abyss planar magnetics sound good too, but, I did not think they warranted the really high price and they are somewhat uncomfortable to me.

For a much cheaper alternative, I liked the top-of-the-line Mad Dog headphones (closed back).

To me, Stax phones border on being too thin and bright and are quite demanding of upstream components. But, apparently, many other listeners demand even brighter sounding phones. If you are one of them, the Sennheiser HD800 headphones will deliver a brighter sound. I personally don't like these phones at all, but, like everything else in audio, this is a matter of taste. You should at least audition these phones and their sonic opposites (Audeze) to get a measure of the range of choices.

Good regional audio shows present great opportunities to hear a wide range of gear. Most shows have a big gathering area dedicated to headphones. This is usually one of the highlights of the show--everyone is friendly and helpful, everything is available for personal trial and the whole scene is enjoyable.

I have older Stax and newer Sennheiser, Audio Technica and Klipsch phones/buds. Each is different and has its charms. If you like the sound of Electrostat speakers or Maagnepan, you will like the Stax and/or other newer ES or planar magnetic headphone options out there as well. Sennheiser tends towards a warmer less bright non-fatiguing kind of sound overall. Klipsch and Audio Technica are both good as well but sound more like most other good phones.

In some ways....better

When choosing phones, don't forget to give how and where you will use them and overall comfort ample consideration in addition to the sound. Like shoes, different styles/designs may be more confortable to wear and work best case by case for different people. That's one big reason among others that there are so many different kinds/styles of phones out there today.