Looking for something super stable. Better battery life would be a sweet bonus!
I'm using CM9.1 and loving it (waiting for CM10stable to test)
The combination of Shostock3 ROM and AJK (former Siyah) kernel seems very popular. I have had it on my phone for a few days already and it has been very stable so far - as opposed to stock 4.0.4 from AT&T that used to freeze/reboot the phone several times a day. The kernel has tons of settings accessible via STweaks app and predefined profiles for performace/battery/etc. The ROM (corresponds to 4.1.2 at present) has the hot multi-view (split screen) feature.
Shostock is based on ROMs from Samsung so all the hardware features (such as HDMI mirroring via MHL) are supported. If you are looking towards more pristine (and up to date) Google experience and don't mind sacrificing few Samsung-specific features (the MHL comes to mind first), AOKP ROM looks very appealing. It is based on CM but borrows many popular features not present in CM from other ROMs. It is also reported to be very stable. The most recent release is the latest Android 4.2.2. I am planning to install it at some point.
Iv'e got SuperNexus JB on mine. I don't use it much since I got the N4, but I took it to Mexico with me on Vacation and it worked great with SUPER battery life.
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