Does power give a like-for-like comparison between different brands of stand mixer? I've noticed that the KitchenAid stand mixers (which are supposed to be one of the best, if not the best, brand out there) have significantly lower power rating than their counterparts from other brands. For example the popular KitchenAid Classic has a power rating of 250W and the KitchenAid Artisan has a power rating of 300W. Even the top-of-the-range KitchenAid Professional stand mixer has a power rating of 325W. Meanwhile, other entry-level stand mixers from Kenwood or other manufacturers have power up to 1000W or 1200W. Is this a true like-for-like comparison (i.e. a 1200W stand mixer from another brand is 4 times better at cutting through a thick mixture than a 300W KitchenAid stand mixer) or is it just one factor among several that could impact the true performance of the stand mixer? Simply put, I was rather surprised at the comparatively low power rating of the KitchenAid products, and thought I must be missing something.
No, the power your mixer consumes is rather meaningless, and I would never use it in a buying decision. Maybe it is in principle possible to construct a bad mixer whose main problem is being underpowered, but since mixer wattage has long fallen victim to Goodheart's law, you can safely assume that everything on the market has sufficient wattage, and if a given model performs badly, it is not due to lack of wattage. Remember, high power consumption is no compensation for shoddy engineering. 

I won't go deep into what you can use for your buying decision instead, since we have a special question for that (linked in the comments). But to hint at it, there is no number available to the customer which would allow for 1:1 comparisons. In fact, not even the numbers known to the producers would allow for such simple comparisons. So don't chase phantoms looking for a number - any kind of number - that tells you how "good" the mixer is.