I currently have the EVO LTE, but had the SGS3 for about 2 days before I returned it. Trying to get my hands on another SGS3 because, well I am a cell phone junkie lol. The LTE has a killer screen, Beats Audio is very nice, great battery life, great camera with affects, and I love the kick stand. What I dont like about the LTE is Sense UI, but that is personal taste. The reason I want the SGS3 is because of Touch Wiz, and nothing else.
At the end of the day, it comes down to personal choice since both phones have their own pros and cons.
Rolling with Sprint since 3/99