I think part of the issue is calibration. If we calibrated screens to look nice, which would be better? I don't have a GS3, but the GS4 is calibrated nicely from what I've seen.
For example my Nexus S calibrated looks amazing and far better than my GS2 despite the Super AMOLED+ getting such high praise.
The Nexus 4 looks like ass, but has pretty good contrast ratios. When calibrated, it looks superb, and in a subjective test against my gf's GS3, I'd say the Nexus 4 looks far better.
Everytime people say IPS sucks, I wonder where that notion comes from. HTC's done a superb job of promoting LCD technology and if you take a look at the Incredible S, HTC One X, and HTC One, they looked superb against their competing AMOLED screens. It's debatable which one is better, but I don't think there's a clear cut victory for either side. If you're judging LCD technology based on the piss poor calibration of the Nexus 4 or Nexus 7 2012, then yeah, it's clear AMOLED is better. It's unfortunate Google gave a bad name for LCD with those. Heck even the Nexus 10's gorgeous screen is ruined with washed out colors.