Personally I lean towards Galaxy S III but I think both are excellent devices. But it's hard to ignore that fantastic battery of the Maxx!
One advantage of Galaxy S III is being released on more carriers, there are probably gonna be a lot more of them in the market & this should lead to more accessories. Given that, someone might come up with an extended battery which still keeps the device reasonably thin!
I also prefer its form and like the physical home key.
But... being on Verizon there have been some reported wifi bugs you should read about before buying one. Don't remember exact details but something about constantly popping up messages about wifi spots & disabling data while it tries to connect.