As far as I know, the "strengths" of the S3 over the HD is the camera and 2 gigs of ram vs 1. The camera is not really that bad, though (much better than what it used to be on the Motorola DROID 3), and I doubt you really "need" those two gigs. Now, what the HD has over the S3: better build, solid feel WITHOUT bring heavy on the hand (fits perfectly mine), not too large while having a reasonably big and clear, vivid display, better battery life (the battery being user irreplaceable is only a problem if you were the multi-battery smartphone user, but you could argue that you don't need to do that anymore), and subjective better looks.
Frankly, the S3 is not ugly, but it does feel terribly flimsy, and I gotta admit, even overpriced for the build quality. Unfortunately, marketing is a powerful tool, and many things which are just very nice are sometimes sold as godly and "must haves". There's nothing wrong with the 3S, of course, but you gotta be aware of reality vs commercial hype when dealing with it-it's just an effective, though rather cheap-feeling phone that has gotten wildly popular through marketing, especially as it's usually deemed as the iPhone's nemesis.
The white HD I have is wonderful, though, and what works for me- try them out and see. If popular opinion matters to you, you'll go for S3 (the "cool" choice, so to speak, though the S4 is now "cooler"), but if it's about what feels good for you as an individual, both phones are really nice, and you will note that the HD is wonderful despite it not being the iconic phone to have that everybody will talk about.
I don't need society's approval, so I chose what works best, looks best, and lasts for m-the RAZR HD (noting that there are also S3 users who don't necessarily chose the S3 just to fit with their peers.) S3 is a nice phone, yes, but not for me for the reasons already mentioned.