My battery life seems to be at least as good under iOS 7 as it was under iOS 6.1.4, if not better. This is on an iPhone 5.
However, I've turned off the new eye candy in iOS 7 (translucency and parallax), and I've turned off background apps and all push notifications as well (I don't need or want things running on the phone unless I'm using them). These are all nice features, but I personally prefer to get longer battery life by turning them off.
I think people who see less battery life are seeing it because they leave new features enabled. Obviously, if you have features that didn't exist before, they're going to use more power, so if you want to return to former power consumption, you may have to turn them off. My guess is that many of the basic features of the phone are slightly more power-efficient than they were in iOS 6 (since that's how operating systems tend to evolve), but the new features are relatively immature so far and are probably still relatively power-hungry.
I have Facebook open a lot in the background and haven't seen a problem, but I disabled push notifications for Facebook, too. It's easy enough to update it when I bring it up on the screen, and I'm not in that much of a rush to see new posts that I have to turn on push notification. More battery savings.