I'm going to post here what I've posted at XDA:
Well I've had my SGS3 for only 2 days and have made my mind up already. I'm keeping the HOX.
As much as I like the SGS3 I just don't like the look of TouchWiz generally. It's features are good as in codec support but Sense has the much better Social Network integration. Simple things like Facebook birthdays in calender and you can directly send a greeting are very useful.
The screens....
My SGS3 has a yellow tint so requested a replacement from Amazon will see if that has it as well. But I can now say I prefer the SLCD2 over the AMOLED. Sure blacks are not as deep and contrast not as great the natural colours are better on the HOX, viewing angles are on par, text appears cleaner and sharper on the HOX and the benefit of a full RGB display and no need to worry about screen burn!
The cameras, both are good but I slightly prefer the HOX for it's lower aperture. SGS3 wins for videos but hopefully some devs can work some magic for high bit recording.
Both feel good in the hand and both look good in the flesh.
Sense vs Touchwiz - Both good for it's own feature set but I prefer Sense. Sense needs to be better optimised as there are microlags where as TW just flies.
SQ - SGS3 wins for headphone out, much nicer sounding and will improve with Voodoo but I've got my original SGS/Sansa Clips as well for music so not a biggie.
Call quality both are good but I think the SGS3 slightly edges it sounding louder.
Speakers - SGS3 is louder but can sound a bit muffled but the HOX volume may not be as high but sounds consistent.
Browsers - SGS3 wins for speed, loads pages quicker and it's faster than HTC. But HTC has text reflow which for me is worth the extra second or so it takes to load so I don't have to zoom in and out on a regular basis. Both have read modes but HTC implement this better with the bigger button to access it.
Battery - Tested the SGS3 on my normal working day conditions, both on their current stock radios and basebands drain battery similar. I can see the SGS3 will last a tad longer and in future with extended batteries will kill off the HOX but the HOX can last me a day anyway and custom kernels and once 3.x sources are out should improve. Teg 3 has the companion core so once better optimised kernels make use of this it should also be better.
Storage - SGS3 wins hands down, nothing more to say.
Development - SGS3 wins for unlocked bootloader. Both phones will have supported devs and the current roms for HOX are fine.
Well to sum it off, both are excellent phones. If I didn't have the HOX I'd be happily pleased with the SGS3 and it's screen but by having the HOX as my main phone since release the screen is just too good to give up.
I will be happy with my HOX and can happily pass by the SGS3 whilst I await another device, especially interested in the Note 2 whenever that comes out as that will be Samsungs high end device.
Both phones are current high end phones, whichever you choose be happy, it's good for Android and good for us as consumers to have this competition. It will only get better and look forward to the next set of phones to play with.