In general, how does price relate to quality?


Surely, there are “giant killers” but, generally speaking, how does price assure one of getting relatively comparable quality? High value applies to many. What do you consider “giant killers”? 
mglik
Sound quality is extremely subjective, so it's tough to correlate price with what you like.  Higher price should at least buy more luxurious aesthetics, and/or more expensive base components.
bdp24 has it right. In general build quality goes up with price but performance after a point does not. Once you get to the best electrical components the builders of "luxury" equipment start adding filigree like CNCed chassis and gold screws. Given that dealer mark up is generally a percentage of the cost the price goes sky rocketing. 
The best values are in the middle somewhere and sometimes they are phenomenal like The Parasound JC1 and 1+, reasonably priced amps that thump many of the megabuck amps. Sound Labs speakers are another great example. Many of us think these speakers are the ultimate regardless of price and they are $200,000 less than their competitors. The Channel D Lino C phono stage for $2600.00 another giant killer.  
You get what you pay for most of the time. Intended purpose of the gear is more important than price.