[Galaxy S III Android Development] BioVolt:
There is no "BEST" rom for "EVERYONE" in my way of thinking, now you may ask why do I say this? Well, this is how I see it :

1. Everybody has different tastes / likes / dislikes (Maybe a rom has a theme you like, maybe it doesn't, this is more of a visual preference and each person will like different things)

2. The next 2 important choices would be :

2.1 Battery saving (These will be roms tailored to giving you longer lasting battery, of course this still depends on how you use the rom, for example you can't expect the battery to last forever if you overclock / use the brightness at 100% / setup the Kernel to use all 4 cores all the time / setup the device incorrectly / and not to forget if you have some rogue app eating away at the battery in the background without your knowledge), these are just some examples, there are many different scenarios.

2.2 Performance based : (These will be roms focused on delivering maximum performance, of course at the cost of shorter battery cycles, this is also influenced by all the points mentioned in 2.1), and needless to say that there will be other factors that influence the performance of such roms which i have not mentioned.

3. Mods / Addons (Lots of roms have the same mods / addons, but once again, this is personal preference, as one of them might include a mod / Addon that you really like / want), please take note of something under this point though : Most mods / addons are created by different authors that have nothing to do with the rom you are flashing, it has just been added to the rom so that you don't have to do it yourself, so what does this mean for you? Well this means that if a mod / addon (and even some themes!) that you like are included on another rom, but not the one you flashed, but you like the rom you flashed and all it is missing to make it perfect for your personal preference is that mod / addon, then search for the thread pertaining to that mod / addon and read how to add it yourself! (Of course not all mods / addons are supported on all custom roms. But don't let that scare you away from trying, as long as you make a nandroid backup before trying to install a mod / addon, you don't have to worry if it doesn't work, you can just restore your backup and try again).

4. Lastly, (Or at least all i can think of right now) : Your choice of rom also depends on things you know / don't know, what do I mean by this? Well, rom authors cannot guarantee that a rom will work as intended for every single person, there are countless factors to consider, and it would be an impossible task, so don't expect miracles! One rom may work great for you, but it might not install / work properly for someone else. (This can be hardware / software / user error related and so much more)

5. A less known factor influencing people's choices in roms, is the size of the rom (This is usually a very small percentage of people who are unfortunate enough to have limits on their downloads), but as unfortunate as download limits are, so is the fact that if you want a rom with loads of options to choose from (Which is usually the reason you are flashing a custom rom in the first place, so that you can have your device looking and working the way you want it and not the way some company decided), you will always be looking at sizes of around 1GB+

So all in all point nb 4. Is the main reason I won't say any specific rom is the best, however I can recommend several roms for you to test and see which one suits you best.

6. Rom's I have personally tested and recommend (Note: These all worked great for me, but as previously stated, this does not guarantee it will work great for you, test them yourself, and when I say "TEST", I don't mean 1 day, testing a rom will require at least 2/3 days minimum, run tests, read the threads, to see if people have bugs, and test to see if you have the same bugs or if you lucky and you don't, also test device throughout the day, by using it as you would normally, and once again, don't be afraid to try things)

6.1 Dragon JB

6.1.1 The good:

Good performance

Good battery

Lots of choices

Mods / Addons

Often updating / fixes

6.1.2 The bad:

Many installation problems reported, but just as many people without installation problems (Hoping that in near future Dragon will split the Rom and Kitchen into 2 separate files in the hopes that this will clear up some of the installation problems, this will also mean that "fixes / updates" which are for the same "BASE" will only need to be changed in kitchen, meaning that you won't have to re download the base, only the kitchen)

Limited theme selection (Can't blame Dragon here, and can't expect him to put in 100's of more hours to not only work on rom but also design whole new themes, but you can use themes made for other roms! If you choose the right ones, or modify them slightly, if in doubt, backup, try theme, if it doesn't work, restore backup) (Also wish some theme designers would join the Dragon team and make some themes specifically for Dragon rom, working with him to keep it updated along with the rom)

6.2 Criskelo JB

6.2.2 The good

Good performance

Good battery

Lots of choices

Mods / Addons

2 Themes

Decent amount of updates / fixes

OTA updates (with on device notification)

Rom & Kitchen (2 separate files)

6.2.3 The bad

Not as super fast / smooth as Dragon / Omega / Turkbey (I have not tested Omega personally, but i was informed by someone who flashed all these roms that Omega felt the "fastest / snoothest") Take note though that this does not guarantee that you will have the same results, you may find that one of the other roms performs better for you!

6.3 Turkbey JB

6.3.1 The good

Good performance

Good battery

Lots of choices

Mods / Addons

Often updating / fixes

6.3.2 The bad

1 theme

No separate kitchen like Dragon, but no reported installation issues

Limited support from author (This just means that rom author doesn't say much but any bugs etc reported on the thread usually result in a new version being released with the relevant fixes, so there is no worries there, also, other users will of course help and offer advice where possible when people run into problems)

6.4 Omega JB

6.4.1 I have not tested this rom personally, but i have heard a lot of good things about it, though I also keep reading their thread and there are a lot of varied results by people, much like Dragon rom, where either it works and it's awesome for you, or you are unlucky and it doesn't work great for you.

Please take all i have said above with a pinch of salt, this is my personal view points and they are only guidelines, as mentioned before, it is all up to" YOU" and your "PERSONAL PREFERENCE", also the good and bad points are only valid for my setup, they may differ on your own devices and setup, and are also prone to change with upcoming updates / versions!

Can't believe I just wrote this all on my S3 lol

Hope i answered your question, and hope you enjoyed the read :P