As someone that has had both phones, I say go with Maxx HD. Similar screen size, still a gorgeous screen quality, amazing battery (I can get 2.5 days), better feel to the phone in general, and better reception.
Alternately, the s3 has a great camera and all the bells and whistles. I averaged about 15 hours on a charge, but had issues occasionally with the battery draining completely in 6hrs. I also had issues with dropped calls and failed messages, which I've never had with Motorola.
In the end you need to figure out what is most important to you in your phone. For me it was battery and reception.