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

The room modes below 50Hz were best avoided by careful speaker and listening position placement in my room. Corner traps helped somewhat along with panels.

Dirac Live with the filter on still sounds markedly better. Mixed phase filters with phase time alignment and magnitude correction creates vivid, lifelike soundstages. The usb signal exits the PC digitally corrected, so no additional A/D anywhere. Agree that deep nulls caused by room modes are not solved by room correction nor are first refllection points, but what about everywhere else? I'm so happy I can flick the Dirac filter switch to on and let my ears decide.

1+ Ralph. As Ralph says no amount of digital correction will fix a standing wave. For most of us you have to use multiple subwoofers. This does not mean that room control does not have a place. The best room control will provide perfectly flat frequency response across the entire audio spectrum and assure that the response from both channels is exactly the same. This gives the best image. From there you can modify the frequency response to taste and do some very cool stuff. My unit has dynamic loudness control. It automatically jumps from one Fletcher Munson curve to the next with changes in volume. It is programmed with 8 Fletcher Munson curves which can be modified to taste. The end result is that the spectral balance remains the same from -40 dB to 0 dB. Bas management is insane. You have independent control over high pass and low pass filters at 1 Hz increments from 0 to 375 Hz with slopes from 1st to 10th order and you can change it all on the fly. The unit will keep nine frequency response curves in memory which you can switch by remote control. My normal curve slopes down from 1 kHz to 6 dB down at 20 kHz. I have another curve down 12 dB at 20 kHz for bright records and another with a 3 kHz notch filter for sibilant records. There is no way you can do these things in the analog world and for those of you worried about resolution this is all done 192 kHz 48 bit.    

What's important (as others have said more verbosely) is to fix the acoustics. It cannot be done with more power.

IMO it is best done by First, positioning listener, main speakers, and subs for smoothest response; Second, adding bass trapping and 1st-reflection treatment if necessary; and Third, using DSP if you want to smooth really low frequencies, say below 80 Hz, further.

In doing all of that, measurement capability (e.g., REW and a calibrated mic) helps a lot.

So, @mijostyn, what unit are you using that does all of that?  I would have guessed a TacT, except those compute at 24 kHz.

1 - Room treatment2 - EQ

In that order.