If you want it now, the S4 would be your best bet for cutting edge hardware/tech, but if you can wait 6 months or so, get the note 3. The note 3 will surely have everything mentioned plus some more refinements to the s pen and its software as well as key lime pie most likely.
I don't see the note getting to much bigger if at all, as they are in a grey area in the market right now. People will eventually say enough is enough and not go any bigger than a certain size, leaving Samsung with a lot of devices on stock that will never move. Also, the rumor as mentioned before of them going to 6 inches just to keep up with a rival company would be a mistake in my opinion. They need to keep their ears open and listen to their customers.
If the note gets any bigger, it will fall into the mini tablet market where Samsung probably doesn't want it.
The next step will be to see if Wacom can make the digitizer work the same at higher resolutions so the note 3 can be 1080p as well.
As for the screens on the S3 and the note 2, after owning both of them, I would have to say that they look great. I can't see the fuzzy text or questionable colors mentioned by people. But sometimes I thing people gripe about things because it makes them feel better. Well, good for them.
Either phone you choose will be a good choice, just weigh the pluses and minuses for your uses or needs. Also keep in mind that people can find new uses for tech on a regular basis to help us in our everyday lives, so newer/better/faster hardware can be a blessing to have.
As you can see from my signature, I Assn in a bit of a quandary as well, S4 or note 3. As I like some of the the S4 apps that were mentioned, the 5" screen and the 13 MP camera, I am going to pass on it for now as I can wait until the note 3 hours, and it should have most of what was mentioned and then some. I also am used to a stylus from my early days of Palm pilots and ipaq's, so they feel natural to me.
Sorry for the long post.
Galaxy S4 or Note 3 for my next. Decisions, decisions.