I have used both the note 3, and Z1 before, personally I would choose the note 3,
Camera in note 3 is slightly better(z1 high megapixels does not mean better quality, the lens does), compare both yourself and look,
much much better battery life in note 3, faster charging, 3.0 usb support.
z1 has a much better build quality than the cheap leather used by the note 3, however it can be fixed with an aftermarket casing.
and of course, z1 waterproof abilities is awesome if you always go swimming :)
The note 3, z1 is that its filled with bloatware, which can be solved by manually disabling them or wait for a stable cyanogenmod rom :)
Custom ROM on note 3 = 0x1 = void warranty
No comparison, Z1 wins hands down, can take pictures of girls in shower, girl can do video call in shower. Or when you are playing watersports with the girl. can note 3 do that?


