What's more important in a difficult room, room correction or higher, clean, power?

The problem with room treatment is the amount of it you need to treat low frequencies, that's where I think DSP can be useful.

This is also where a distributed bass array like the Swarm is helpful.

In my 12 * 22 * 7 foot room, with an additional space under the basement stairs that makes the room L shaped, I got pretty good bass definition with my Vandersteen 5A Carbons. But there were some bad dips between 72 and 120 hz that I could not sufficiently smooth out, up to at least 10 dB below 70, the middle point on my meter. So I purchased three GIK Acoustics Soffit bass traps that I placed at the two corners on either side of the speakers, arranged on the long wall, and one directly behind my chair, in the nook under the basement stairs, where there was a lot of bass buildup. A few weeks later when I had some free time, I readjusted the bass on the speakers. The results showed some smoothing in the measured frequencies, but there were still some dips in that 72 to 120 hz range that I could not correct, which remained down 8 to 10 dB. However, I was not prepared for how dramatic the improvement was in terms of slam. The lower bass is dramatically more powerful and cleaner. Even with the equalized bass, that was not good enough to achieve what I’m hearing now. So, I can definitely vouch for room treatment! Aesthetically speaking, I’m done. I could probably get even better results with more traps, but I don’t want any more traps in my room.

Re the OP’s scanario:

"Tryin’ to get high, without having to pay..." -Marianne Faithfull

Room correction is not a fix, the effect of the room problems still exist and would still be interfering. It’s like a continual hasty pasting over of an ongoing audio murder.

Room correction can be done judiciously, minimally...and then one has to figure out if the given minimal corrections are worth the problem of interference in signal purity that is brought about via the installation and use of the hardware the creates the corrections.

Then to understand such under the given signal disturbances and coloration that is carried out by the choices in the rest of the gear that is in the room.

physical acoustic correction via physically correcting the room is the best bet, every time and likely always will be. It is just the nature of how acoustics and audio works... that makes active correction suitable for non fidelity situations like concerts, malls, airports, bars, commercial theaters, etc...places where fidelity is not the primary concern.

If DSP was the fix that it is advertised to be by some, then it would have taken over the high fidelity world by storm.

Even though it has been around for quite some time, note that it has not taken over.

Thus, thinking cap..a bit of funds...some work..and fix acoustics.

IF this cannot be done, then the room must be accepted as it is, or try some minimal DSP correction, with the caveat that the carrier of the DSP, the digital systems involved - are destructive to overall fidelity.

One can fix some of the annoying bits with the DSP and then find themselves listening less and less to music in that space, as the positives are outweighed by the negatives of the digital manipulation. Negatives that take time to consciously discern and put label to.

I have had room correction based subwoofers and they are limited as to what they can correct in the bass response.  
They definitely do not satisfactorily correct issues that are caused by poor fundamental integration between room and main speakers.  
Fundamentals include best position in room for main speakers, best position for subwoofer, proper subwoofer crossover frequency and phase and proper subwoofer level.  
Once these were set well the sound was excellent and I could not tell any difference when room correction was engaged.  
My recommendation would be to get some RTA software (phone, laptop or tablet) and a CD with full bandwidth pink noise and start measuring the response and then adjust positions, crossover, phase etc until you have a smooth response.  It is always comforting to know your response is smooth.    Then "season" to taste, slight adjustments in level to suit your preferences.