Basically the OS skin adds several features not found on other branded phones. For example, on a Samsung phone, you have access to 20 quick toggles right from the notification bar. Other branded phones don't have that out of the box because it's a Samsung thing.
Yeah, you only get a dozen on the HTC One or One X (with the JB 4.2.2 update).
Though there are power control apps in the market that can give you this even without root now. So 1 minute's work gives you that on any phone.
Seriously? There aren't many other flagship devices which offer both removable battery and microSD card (non-flagship there are still plenty). And Samsung put a lot of extra features in which are either cool and amazing or pointless gimmicky bloat, depending on your tastes. They probably have implemented high-MPix cameras better than LG or Sony, from the samples I've seen (but pixel count is only a small part of the story with imaging, so beware of people equating that number with quality). If you like AMOLED screens then there's that, though Motorola also use them (the Moto X's non-pentile 720p should be better than the SGS3's screen, though as the X hasn't crossed the Atlantic I can't verify that myself).
But to be honest, I don't think it does stand apart from other JB handsets. In my judgement it's a well put-together package, designed somewhat with an eye to the spec sheet (the "big numbers" school of marketing). It certainly deserves to be up there with the other flagships, but I wouldn't say it's overall better (obviously, because I bought something else!). The S4 Active was more appealing to me, but that will have a smaller developer base (which is a factor for me).
But I would also say that that doesn't matter at all. The important point isn't what's "best", and certainly not what other people think is best, but what you are happiest with. So I'd echo Rx's advice - go and play with a few handsets and see what appeals to you.