They change constantly, websites don't really sell bitcoin to you, not generally, there are some of them but they are rare and not liked by many people. Generally speaking exchanges are places where you exchange your coins with others not with the website directly. Hence that creates a situation where sometimes one website is cheaper, sometimes the other website is cheaper.

That is why there is no website that is constantly under pricing any other website because they can't really change the prices themselves. If you asked the exchange owners they would prefer to be the cheapest exchange out there since that would bring in more volume and trade fee's for them but if you are too low for a while, people who do arbitrage will close that gap rather quickly and you will be back on track.