iOS 7 was recently released and delivered various changes including some bugs but ultimately made devices faster. For Android, there are several ways to boost performance and rooting is not required.
Making It Snappy
Most Android devices sold in the market features Developer Options in the Settings menu. It is usually found on all Android devices running Android 4.0 and above, but hidden on some models. If it is not visible, go to Settings > About device > Tap the build number seven times. Now proceed to the Developer Options and select Window Animation Scale, Transition Animation Scale and Animator Animation Scale. Turn them off or set to 0.5 instead to bring out the snappy feeling.
RAM management can be very difficult, especially for devices with 1 GB memory. You can help out the RAM by logging out manually on social apps if you do not use them often. Another way is to remove apps you do not usually use to free some memory. You can also disable apps on the Settings if you cannot remove the app.
Widgets are beautiful, but can turn any mid-range device sluggish. Limit the number of widgets you put on the lock screen and home screen to speed up overall loading time.
If you think the default launcher is too slow, get something else from the Play Store. There are several great launchers such as Nova and Apex which are light on the RAM and loads faster than the stock version.
Careful on Live Wallpapers
Live wallpapers are animated and if you enable one on the home screen, your RAM may suffer depending on how good it was scripted for Android. Select live wallpapers with fewer graphic or modify elements to reduce RAM consumption.
Like a computer, smartphones and tablets require some reboot from time to time. This is much recommended to free space on the RAM and clear caches. On every full recharge, reboot your device once.
Selecting New Tasker
There are some task managing apps that are good such as Clean Master for Sony Xperia devices. It features RAM management, cache cleaner and antivirus in one package. It does not impede overall performance while helping clean out bulk items on your device.