The main thing is that I really don't want a phone that I need a belt clip/case to carry around. There's no way a screen that large is going to work out well in jeans and slacks going up and down the stairs and hills at school. I'll watch the last vid posted above and see how it sways me, but the footprint of the Note 3 and Z1 are my main concerns with either. I guess they have to give you a reason to go to the Note 3, but the design of the Note 3--shape wise--in an S4 footprint with S-pen functionality is what I really want.
I will say that one major point of value would be not having to pull out my laptop for most things. One of the guys in a morning class I have uses his S4 for almost everything in that regard, so something slightly larger, faster, and with a brighter screen and more functionality wouldn't be the worst thing ever. That is going to be a lot of real estate for me to do my custom home screens on though =p