Has anyone had troubles with an iPhone 4's battery life failing after upgrading from iOS 6 to iOS 7?
There are a few reasons iOS 7.1 upgrade slows down your iPhone 4/4S.

http://www.imore.com/top-5-tips-speed-iphone-4-or-iphone-4s-running-ios-7


Background app refresh
Transparency and motion/Parallax


Have you tried disabling these?