These are my 5 favorite roms that i have yet to use. Some give you fast experience and some also give lots of customization
this rom is very fast and also gives a nice look to your phone check out my video review on it.
4. Urban Karnage Rom
This gives you touchwiz and some 4.2 apps which makes this rom great. You also get KT Kernel and lots of other tweaks.
3. JellyBam Rom
This mixes Paranoid, Aokp, Cyanogenmod, and Touchwiz. The Customization is endless.
2. Serenity Rom
This was the first touchwiz Jellybean rom and it makes your S3 have features the Note 2 has. it is a great and fast rom.
1. Illusion Rom (CM 10.1)
This gives you stock android, jellybean 4.2.1, and alot of tweaks making your phone be as fast as it can.