Every iOS upgrade has three possible effects on the iPhone/iPad's battery: it causes the battery to drain faster, it improves the battery or it has no effect on the battery.
Just because someone with a voice and readership says his iPhone's battery is now performing better – after updating to iOS 7.1.1 – doesn't mean it holds good for all. There are obviously users who face new battery issues (faster draining) after the update.
iOS 7.1.1 Battery
The general consensus seems to be that there are no noticeable changes to the battery life on all devices – iPhones and iPads. Most polls seem to indicate that amongst a majority of the users, iOS 7.1.1 update hasn't impacted the battery.
But there's also a section of the users who report better battery performances. I noticed that most of these people are on iPhone 5 or 5s. The code, while not detailing any tweaks to performance optimization, seems to have included some kind of an optimization that would use lesser resources of your iPhone 5/5s.
And then there are users who have had their iPhones drain the battery faster even when minimal services are running on it. Again, I noticed this on iPhone 4s more than any other device.
As far as iPads and minis are concerned, the battery seems to be working good – either as before or, in some cases, slightly better.
Fixing battery issues
There's a lot of stuff we've already addressed about battery issues in iOS 7.x. There are no hard rules or static how-tos to get better battery performances but you try a set of things – in random order – to improve the battery life of your iPhone or iPad.
Here's what you can do to fix battery issues on an iPhone 5. The processes can also be used on other devices like iPhone 4s and 4.
The suggestions given in this post about iOS 7 battery life also hold good for iOS 7.1.1.