iOS 7.1 is, no doubt, outstanding and arguably what 7.0 should have been. But as with any iOS update, it has a tendency to drain your device's battery faster than previous versions, unless you think carefully about which features you are actually using, and which are just pointlessly draining it.
The biggest two of these are:
I'm not saying you shouldn't use these, of course. Frankly your iPhone and iPad are seriously hobbled if you don't. Pretty much every article I've seen on this topic recommends nothing more than checking Settings > Location Services to ensure that no apps are using Location, that shouldn't be.
Good advice no doubt, but in my experience this is of limited use. Most apps that ask to use location do so for a reason, and you severely limit them if you deny it. My better advice would be - just pay attention to which apps you keep running in the background and close those you arent using. This has a much bigger effect on your battery life, and you'd be amazed how many people just never close their apps. Personally I have OCD about this (as with so much else in my life).
In case you are unaware of this - double-tap the home button or use an upwards four-finger swipe to show you thumbnails of every app running in the background (which if you are unaware of this, is probably every app you've ever opened). Close each one by swiping up on the thumbnail, and watch it disappear.
Background App Refresh
This was new with iOS 7. Essentially, while enabled (which is the default), your apps will refresh themselves in the background while you work in other apps. Facebook, for example, will regularly poll the server to ensure that when you return, those hilarious selfies of your niece and her lunch will be there waiting for you.
I'm sure this has use cases - I just can't think of any that are meaningful to me personally. I'm fine with the idea that when I return to an app, it will refresh at that point. I use very few apps that require such large quantities of data that I'd be waiting more than a couple of seconds. And for those that do, do I really want that app downloading that amount of data every few minutes when I'm not looking at it?
So in both cases - it's the apps that are running in the background that are killing your battery. Pay attention to those, and you will significantly extend your juice.