One man's opinion...
I'll start by saying that I own an Axe Fx and Line 6 gear, as well as a variety of modeling software. I have a number of good cabinet IR's. I am also very adept at programming these and have tweaked them to the nth degree to get the best out of them for myself and some other artists. This has often included many iterations of A/Bing between my real world amps and the emulations that I was programming. I fully understand the "in the room" issue that many discussions of modelers versus tube amps include.
In my experience, the results with digital can vary, depending upon application and on the particular modeler. At its best, I've gotten very good, even great recorded tones. However, even at its best, it does not (to these ears and hands) feel the same nor sound the same as a great tube amp. I still greatly prefer playing my tube amps, both live where I can turn them up and at home where I'm much more limited. The feel is much more enjoyable to me and the sound is much more inspiring. To the average listener? Meh... The average listener streams Beiber on Spotify through cheap, consumer level DAC into Bose speakers, so they get no say! Ha! ;-)
I have the modeling tools for when the desire for convenience outweighs preference. Although I find myself moving away from modeling, in general, and in the directions of direct recording utilizing my tube amps with active load boxes and cabinet IR's.
In my mind, a tube amp isn't a guarantee for better tone over a modeler... Tone comes from the player as well as the equipment, and relies upon other elements and skill for proper live sound reproduction and/or recording. Also, there certainly are a lot of mediocre (or worse) tube amps, a lot of poor recordings of tube amps, and a lot of players who's playing doesn't exactly flatter the amp designer's work.
But, I think if we are comparing each option at its best, with good playing skills in tow, then (for me, at least), tubes continue to rule by a large margin for both tone and feel.
I know that there are those who feel that certain high end modelers emulate tubes to such a degree that they find the differences imperceptible. I believe that these people are telling the truth, but with the caveat that their sensitivity to the differences are not as heightened as some others and/or they are not as nuanced in their playing, so as to better reveal these differences. That's not a slag against anyone, it just reinforces that there is not one ideal solution for everyone, as we all have different perceptions, preferences, playing styles, and levels of mastery of our instruments. We all need to find what works for each of us.
I think also that the differences are accentuated with certain tones and styles of playing. For instance, mid gain and verge of breakup sounds and intricate playing will spotlight the differences more so than, say, high gain or hyper clean tones and simpler rhythm playing.
What digital has in its favor is versatility with regards to base tones, fx, etc, ability for storing large amounts or presets to be recalled instantly, great depths of tweakability, and often portability (although sometimes after a FFFR amplification solution is considered, portability may not be better). Also, for many it is easier to get a good recorded tone with something like an Axe Fx than a tube amp in a room with mics, so that should be considered if it applies.
Tube amps sometimes offer easier repairability (certainly, older classic PTP circuits are).
With the addition of devices such as the Bad Cat Unleash and better implementations of PPIMV's, big tube amps are more usable than ever, and even for low volume applications, big (even classic NMV circuit) amps are an option for home or live use. It's no longer a matter of choosing between a digital solution or a small tube amp (which, for better or worse, do not sound like there big brothers). With the addition of devices such as the Two Notes Torpedo offerings and Suhr's Reactive Load, silent/direct recording is also an option, even with big tube amps. So, the convenience gap of digital versus tubes has narrowed significantly.
The biggest challenge, IMHO, with tube amps is with the availability of tubes themselves. Tubes are a niche commodity and only manufactured in a handful of places in the world. The tools are aging and the knowledge is dying out as this is not something included in modern engineering and manufacturing education programs. NOS tubes are being bought up and used up. Perhaps we may one day see digital emulations of actual tubes that plug and play into tube amps that model the physical characteristic of these lovable glass bottles (however the market for this is so slight, I would be a bit surprised).
So, the answer is now as it always was, I think... It's really whatever you personally like best. =-)
Cheers,