How to judge an amplifier's performance with a "powered-woofer" speaker?

ALL speakers (with/without bass amplification) holistically respond to amp changes, and they are typically immediately discernible. See for yourself. Powered bass readily responds to speaker cable changes and power cord changes. Ditto for subwoofers. 

The Legacy Audio Valor Speaker System I reviewed for Dagogo.com, with its internal bass and subwoofer amplification, responded just as any passive speaker would to amp changes on the mid/treble. 
Even if  the change is to the midrange on up, the entire speaker will sound distinctly different due to the change in interaction between the drivers. The relative strength of the bass, it's tonality, dynamic power, etc. relative to the mid and treble has changed. 

This thread is fine evidence of the hubris of readers who default to distrust of reviewers, thinking they know better. Well, in the majority of cases, you don't.  :)

I have no interest in the particular review or reviewer,  but in general  another aspect to be discussed with powered bass is the signal cable and power cords. Many never maximize their speaker due to being too arrogant,  lazy, or chintzy ( or all 3) regarding those cables.

Once or twice I tried to get powered model and passive model for side by side comparison,  but manufacturer was unwilling.

You can't have it both ways, obviously. My point is that the typical audiophile would think that not much would happen to the bass response of a speaker with onboard amplification for the bass. That is wrong, and typically the perception of the entire speaker's performance, including the LF, is reoriented through changing amps. 

To address the concern of the OP, if, perhaps he is considering the amp in question, I have not found typically that an amp that performed better with a fully passive speaker did more poorly with one having powered bass. In my experience, usually, an amp is superior/inferior in entirety. It is quite uncommon for an amp that would not drive a passive speaker well in the low frequencies to be superb in the mid/upper. So much of the performance is shaped by frequencies above 100Hz that you will by and large have the character of the amp regardless of the speaker being active/passive bass  (Some will disagree, no doubt, but I am not interested in arguing that point). Imo, one might think that a lower powered amp would be superior in such an application (powering the M/T) as a speaker with powered bass. No, you have no clue until you compare, and when I have done such comparisons, the superior amp with passive speakers has been superior with speakers having active bass. I have typically enjoyed the headroom afforded by higher powered amps to lower powered in such applications.

So, perhaps that summary helps the OP understand why a reviewer would pursue such a system and comment on the bass. Technically it is correct that the internal amp would power the bass, but the experience is holistically different, and valid when comparing amps. 

The same holds true of powered subwoofers; the perception of their performance is changed strikingly by swapping out the mains amp, even if no power cord or signal cable is changed to the sub. Again, amps that did better with solo main speakers typically also did better when the subs were added. 

That is not to say you can't massage the sound of the passive or active to make one sound better than the other.