There are things you can try to speed things up on older hardware:
As well as the ideas above you should also ensure you have Settings/Accessibility/Reduce Motion [on] and don't use any of the Dynamic wallpapers, these both use more CPU than you can really spare on an iPhone 4. Check you don't have location services enabled for any apps that don't really need it too. Ditto for iCloud.
Although performance on an iPhone 4 is never going to be as good as on a 5/5c or 5s it shouldn't be that slow, if you do some digging and configuring you should be able to improve its performance considerably. iOS 7 is quite useable on an iPhone 4 when configured correctly.