I was just playing with one yesterday at Best Buy. Even in indoor lighting and the brightness maxed (I checked) the screen seemed dim and dingy. The colors are certainly extreme but they're not as bright, so somehow they didn't seem more "vibrant" to me. Also the screen in general seemed grainier...not sure if this is partly due to the pentile tech, the lower ppi, or the lack of brightness.
To the poster who said he showed all his friends the note II and they were "blown away" by the screen - either they were reacting to the size (and I'll admit I'd like a bigger iPhone) or they are just suckers for crazy kool-aid colours and don't notice the overall quality.
I've tried several phones with AMOLED screens, and none of them looked as good as an IPS display. Blacks were great, but that was it.
I played with a GS3 in the store and found it to look dim and dingy as well. Besides that, the white balance is way too cool, and colors don't look right. Maybe with calibration it would look better. I've never seen one that has a custom calibration.
I had a Galaxy Nexus last year, for one week, and felt the same about it. I even used the same term as you, dingy, to describe it.
Here is my post from a year ago.
https://forums.macrumors.com/posts/14135576/
Edit: Oh, and I can still tell that the GS3 has a Pentile screen, and I find that annoying too. Maybe at 1080 that will finally become unnoticeable.