About my phones OS:
I'm using 3rd party ROM, called Paranoid Android 3+, or PA3+ in short version. Main reason for flashing custom ROM over official Samasung Galaxy SIII was that Samsung ROM is very huge with lot of unnecessary features, which slows down phone to critical levels. I allways had like 1-2 second lagspikes on every action. But with PA3+ everything works smooth.
PA3+ is based on 4.3 android, but newest version for Galaxy SIII official ROM is 4.2.1 or something like that.
Also PA3+ comes with bunch of great features, one of biggest features is Hybrid mode. I have 1280x720 resolution display and yet i can only use it as phone. Hybrid mode lets me use my phone as regular phone, as phablet (hybrid version of phone and tablet GUI) and as tablet. which is great, having that little tablet toolbar and small toolboxes, which don't cover whole display. Also you have homescreen rotation with this great feature. And you can chose your resolution, if you are stylus fan or gave small fingers, you can set the highest resulution and get full experience from your huge display resolution.
Another great feature is HALO. basically is something like multitaskng. Main usage for it is- for example, you are browsing web, watching movei or just playing a game. While you are doing thet you receive text message, and HALO allows you to read SMS and respond in smaller popup window without closing anything what is in background. after you respond, just tap outside hallo box and you are good to continue what you were doing before.
PA3+ is very powerfull and fast ROM, definatly something to consider if you feel like your original ROM is way too slow for you. For me- I'm enthusiast and I like to change something new, tweak my phone around to get best performance and experience. As far as I can say- PA3+ is one of the best ROMs out there. Guys from Paranoid team has done brilliant job.
Little bit about downsides.
battery life time- with orginal ROM i had built in power saver, which was really good. My phone was running about 2 days with 1 charging (mainly used it for calls and SMS), now with 3rd party power saver I still have to charge daily, which I guess is normal for such a powerfull smartphone, but still I haven't found 3rd party power saver as good as Samsung built-in.
PA3+ uses default anddroid launcher. Not really downside, but still, someone would prefer custom launcher. But I guess, you can still install GoLauncher or something like that. Haven't really tried that.
Stability- I get some crashes once in a while.