The Nexus 7 was the first Android/Nexus device to ship with Chrome as the stock browser. With Android 4.2 and the Nexus 4, Google completely ditched the AOSP browser and made Chrome the new default browser. While Chrome for Android is an excellent browser, it has some serious performance issues on slightly older devices. It feels a bit bloated and is a memory hog compared to the AOSP browser. Apart from performance issues, Chrome for Android clearly struggles on some heavier sites like TheVerge, where pinch-to-zoom is choppy. It is also visibly slower than the iOS6 and AOSP browser in benchmarks.
Thankfully, many custom ROMs for the Nexus 4, including CyanogenMod and AOKP, still include the AOSP browser as an alternative to Chrome. However, if you are running the stock Android 4.2.1 build on your Nexus 4 with root access, you can easily install the stock AOSP browser in just a few steps.
Step 1: Download the browser.apk file from here, and transfer it to your phone.
Step 2: Copy the browser.apk file to the /system/app folder. Then, long press the apk and select the option to change its ‘Permissions’. Change the permission of the APK to -rw-rw-r.
Step 3: Rename ‘BrowserProviderProxy.apk’ and ‘BrowserProviderProxy.odex’ to something. Otherwise, the AOSP browser will just force close.
Also, keep in mind that once you change the name of these files, you will not receive any OTA updates in the future. You will need to rename these files back to their original name, if you want to receive the OTA update.
The AOSP browser also supports Flash, which Chrome lacks. Simply download and install the Flash Player APK from here, to enjoy Flash based websites on your Nexus 4.