I would go with the Maxx HD for several reasons. Now, take my opinion like anyone else, but I have used almost every phone out there and I am returning to the Maxx HD. Here are the phones I have used in the last 5-6 years. Treo 650, Treo 700p, Blackberry 8830, Blackbery Storm 2, Blackberry Torch, Palm Pre, HP Pre3, iPhone 3G, iPhone 4, iPhone 4S, iPhone 5, HTC Evo 4G, HTC Evo 4G LTE, Razr Maxx HD, Samsung Nexus 4G, Samsung Galaxy Nexus, Samsung Galaxy S3. As you can see with the exception of windows phones I have used pretty much everything.
The phones I like the best out of all of them are the Pre3 (best OS but no support any more and apps were non existent), iPhone 5 (fast, decent battery life, easy to travel with if on Verizon or Sprint, tons of apps, but smallish screen) and the Razr Maxx HD (great battery life, tons of apps, easy to travel with, large screen, best OS next to WebOS).
The things I do not like on the S3 that I have been using the last day and a half and why I am exchanging it for a Razr Maxx HD are:
Battery life good, but not close to the Maxx
Cannot change APN for international travel without rooting
Touch Wiz (I Hate it). Even when I loaded a different launcher I still have the crap in the notification pull down. Could they make the toggles any larger?
Build Quality not there
The antenna is not as strong. At home on the Maxx HD I could easily carry a conversation. In the 3 calls I have made on the S3 I have dropped calls 12 times requiring me to call people back. 12 times in a total of 20 minutes is unacceptable.