Though the AOSP browser might lack some nifty features that Chrome offers, it works just fine on all devices and will be quite smooth on low spec devices. If you would like to get back the old AOSP browser on your KitKat phone, read below simple tutorial. Installation Guide:
Download the “signedbrowser.apk” file and place it in your phone’s internal or external storage. (Download it from source here)
Open any file explorer on your phone and navigate to System -> Apps folder. For example, if you are using ES File explorer, go to Devices -> System -> Apps.
In the Apps folder, locate “BrowserProviderProxy.apk” and install it. Yes, the installation will fail, but it is normal. Then reboot your phone.
After rebooting, install “signedbrowser.apk” file that you have placed on your SD card. Do not forget to check “unknown sources” from phone’s Settings -> Security. That’s it. Please note that, Flash player will not work with this browser on KitKat phones. If you would like to have a faster browser on your Android phone, I am sure you will love this guide. (source)