I actually did the opposite, I exchanged my S3 for an HOX. I have the S3 for about two weeks and the HOX for about a week and what I've noticed is that the HOX had a better battery life and a better screen. I was using both phone heavily too.
The S3 was too light and felt way too cheap considering the price I was paying, the HOX feels like such a premium phone in the hands. The S3 felt like it was going to shatter if I dropped it from any height. The HOX feels like it won't break after the first drop.
The screen on the HOX is better than the S3. Don't get me wrong, the display on the S3 was great but the HOX has an even better one.
When I use the multitasking button, it takes me back to exactly where I was before. It doesn't start the app over or anything.
The only real advantage I see the S3 has over the HOX is that it has expandable storage - but then again the HOX has dropbox to store files. And the S3 has a removable battery and the HOX doesn't.
All in all, I'm so glad I exchanged phones, the HOX is such a sleek and sexy phone. It doesn't feel like a toy from Toys-R-Us that my 3 year old cousin is going to play with.