I agree...current is more important than wattage when it comes to real world speaker loads, especially difficult loads. That's where all of these AVR's just give up.
As I have explained in detail to dlaloum before but failed to convince him, that such statement, while not incorrect, is misleading and over time, would help sustain audio myths.
The fact is, such statement naturally implies that, given the choice of more power ("wattage" as you call it), and more current (amperage), the latter is more important. This is not true at all as a general statement if one looks into the relationship of voltage, current, power, phase angle, and distortion factor (not as define in audio but in power systems). To say one is more important than the other over simplify something that is more complicated.
Take a look of the basic formula involved:
Power = Voltage X Current X power factor (we can practically ignore the distortion factor in audio).
Current = Voltage/Resistance (I'll use resistance because most bench test labs used resistor load)
So, you can't single out just one, as current and voltage goes hand in hand, and both have to be considered.
Take a look of one quick numerical example:
Specs on power amp output side:
Amplifier A: Rated max voltage 30 V, max current 30 A
Amplifier B: Rated max voltage 60 V, max current 15A
So both amps can be rated 900 VA, probably about 720 W based on a typical 0.8 power factor used if the manufacturer rated it in "wattage".
Which one is better, are you going to take Amplifier A because current is more important? Obviously not, because it depends on your application. In fact, for the vast majority of usage, where speakers with nominal impedance say, 6 ohms with dips to 3.5 ohms, I would take Amplifier B if I actually need as much as 700 W to ensure my amp will not run too close to its clipping point.
My point to dlaloum (he has speakers that have impedance characteristics that are not very common at all) is that while he is correct in emphasizing the importance of current especially in his use case, it is better to include some caveat so as not to help perpetuate the misconception of the so call high current amp thing.
Case in point, and as evidence, Harman Kardon is one of those that really emphasized in the 90 to early 20's, that their AVRs are high current, often claiming 40 A, or even 60 A. To be fair though, if I remember right, they did include the caveat, that those were instantaneous values, but still it helped create the misconception that their typically lower "wattage" AVRs vs Denon, Yamaha, and Sony's in the same price range, are actually better, to the point many thought not all watts are the same blablabla.. Such misconception still persist as evidenced in many forums even on the generally more technically oriented sites, such as Audioholics and ASR.