[Verizon Samsung Galaxy S III] Neverendingxsin:
Well there's two routes you can go to get your JellyBean fix, and that's either AOSP or TouchWiz.

Touchwiz: You've got two choices.

- You could go with Synergy JB 0.2 beta which is based off the AT&T leaked JB touchwiz build. I personally have not ran it so i can't comment on how well it works, but i use synergy as my touchwiz choice of roms, and was never disappointed by there work, so i'm sure the JB build is working great.

- There is also Jellywiz which is made by Incubus, he's been basing his off the latest leaks, and has a few builds out. One of them is a custom build which just has a few theme changes, and a few other things added in/changed. There's a lot of praise in that thread for his rom, the only bug i had when trying it was that i could not get voice and data to work at the same time (phone calls and web browsing at the same time) But that is because its not based off a verizon leak and until then probably will not work.

AOSP: We'll you've got a lot of options, there's a few here on XDA and then some more on Rootzwiki, so i won't be giving detail on all of them, just a few. But they will all generally 'look' the same, by that i mean because they are all based on AOSP source it'll have the same look to it, since source looks the same.

-CM10: Well it's your basic CM that you've grown to love (or hate :P) you can expect nightlies, and things to get fixed in a timely matter. If you used CM7 or CM9 on previous devices then you'll know exactly what to expect. Its built directly from source and you can expect it to be speedy quick.

-AOKP: It's built from source as well just like CM10, but has more options in it, and generally more customization as well. If you use it it'll look a lot like CM10, but it'll have added in bonuses :)

-CodeNameAndroid: Again built from source, but with codename you've got a ton of customization thrown in, there's a lot of stuff from different AOSP options thrown into it. Right now the Navbar doesn't work without flashing a separate file, but that's not a huge problem since its just a little file to flash. I personally am using it right now and its been great to me, can't really complain about it at all :)

-LiquidSmooth: Built from source, those that have used a liquid rom before will know exactly what to expect. It will be speedy quick and smooth as hell. You'll find plenty of butter in it as well, they've got there own liquidsettings that'll allow you to do even more customization, and i give them major props, i've currently got them going on my old thunderbolt which is my backup phone, but also used them on my OG Droid and i can vouch that they will provide an amazing rom for users :)

There are more AOSP Roms over on rootzwiki, but its again the same general thing, each AOSP rom comes from source, but each developer will theme/modify/add/remove/customize to there own liking to provide you with what they feel is the best user experience. The biggest difference between the Touchwiz JB roms and AOSP is that with AOSP you'll have a lot more options going and it'll be stock jellybean, no touchwiz nonsense to hold you back. Some people love the touchwiz stuff and that's fine, but some will love having pure jellybean on there phone and being able to take advantage of that. I'll tell you honestly 100% that AOSP will be faster no matter what touchwiz rom you run.

Oh and kernel wise, i fully stand behind imoseyon's lean kernel for AOSP roms, i've always used imoseyon's kernel's and have always gotten amazing battery life on my GS3 and thunderbolt.

Phew i really hope this helps you with any decision you may have :)

***If i missed any Touchwiz or AOSP roms i do apologize, i don't know them all off the top of my head, so please don't think that just because i left yours out that i meant it in a bad way***