1. I believe razing the city nets you loot/pillage golds and that's it.
2. Installing a puppet government means you gain the income/research etc from the city but you have NO CONTROL over what it builds, the puppet governor controls that. On the upside, you suffer much much less unhappiness by choosing this option.
Oh my fucking God, that is awesome. I have always, always wanted some option when conquering an opponent's nation beyond just a zero-sum battle for each and every city. Finally, I can deny him the possession, to my benefit no less, without making myself responsible for the aftermath.
**Why should you care about the unhappiness of a new city? Because happiness is no longer tracked per-city. Happiness is now a global civilization modifier, and you must keep your citizens' happiness balanced with your expansion and military actions else you will face large-scale revolt. Unhappy cities are a large drag on your empire, and this gives you much more incentive to resolve the unhappiness where in Civ 4 if a city was unhappy you could (mostly) safely ignore it until it fixed itself.
This however I'm not so sure about. The otherwise excellent knock-off
Call to Power did the same thing, and I hated it. You couldn't tailor your policies below the national level, you could only effect the happiness of cities with the stuff built there. If any one city lacked enough stuff to keep it happy, you had to change the policy of the entire nation until it caught up in development, making founding new cities after the Bronze Age a serious chore. On top of all the requisite complaints about cities acting as a Happiness Hivemind being terribly unrealistic.