Well, considering this isn't the Sprint section, I'm not going to assume that the Evo is an option for you. Although I will say that I am on Sprint and I had the same concern in deciding to get the Evo LTE or Galaxy SIII. After some intense research I finally decided that the Galaxy SIII was the phone that best suited my needs. As for the screen on the SIII, I've been VERY pleasantly surprised. Yes, the Evo screen is likely better, but that doesn't mean the SIII screen is bad. I did have to turn off automatic brightness and download a third party brightness toggle for my home screen. There hasn't been one moment outside that I haven't been able to see my phone and the screen watching a HD clip is stunning.
Hope that helps....