Here in SF, as I understand it there were a lot of tax subsidies to bring Twitter and other companies here into the city. Now the city is booming, and although that has caused other problems like strain on infrastructure and housing, these are solvable problems. They seem like much better problems to have than a failing economy. (Not to mention, they have much deeper causes as well that should have been addressed regardless, it's just that now it's become quite urgent).
As another data point, there was a good Freakonomics podcast recently with the governor of Rhode Island, and she basically claimed that tax incentives to bring companies like GE into the state (in addition to other programs like job training) were responsible for the economic turn-around they've seen. Over the past few years they've gone from having one of the worst unemployment rates to somewhere around average for the country.
Rather than knee-jerk oppose this competition, it seems like we should move the conversation to "Okay, you're offering these tax incentives for Amazon. Now you need to commit to building enough housing to meet their projected job growth at HQ2 over the next decade, as well as a public transportation plan to keep up with it."