I debated over the decision and ended up with the Maxx HD for two principal reasons. I need a phone and data network which works, even in marginal signal locations, and I need it to go all day. All the other features are great, but secondary. I never owned the S3, but have heard and read complaints concerning the ability of the S3 to hold calls and data in areas with weaker signals. There are enough complaints out there to create reasonable concern. One the other hand, the Razr Maxx HD has lived up to its reputation as one with strong reception and build quality. I have not had one dropped call since getting it one month ago, even in areas my Thunderbolt had issues or where my daughters IPHONE 5 currently struggles. Additionally, I am a fairly heavy user and yet have not run this thing out of juice. Even with the ugly extended battery on my Thunderbolt, there were days the battery ran out. Not with the Maxx HD. If you need your phone to be a work horse first and all else is secondary, the Maxx HD does not disappoint!
On a side note. I am a photographer and unless you are really enlarging the photos from any cell phone, let alone the S3 vr Maxx HD, quality differences are barely discernible. Yes, they do exist (mainly in the shadows) but are not visible for 99.99% of photos taken and sent with cell phone cameras. Between the S3 and Maxx HD, the cameral quality difference should not be the deciding factor for which phone to purchase... no one will be able to tell which phone took which picture unless they print and enlarge a low light picture larger then 8x10 in. If your intention is to that regularly, it is doubtful you will be relying on the cell phone camera. Despite all that is written, camera quality should not be the deciding factor between the S3 and the Razr Maxx HD.