Does power give a like-for-like comparison between different brands of stand mixer?
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.