The Note 2 and Note 3 are, based on my observation, good for a couple days without charging. Like the iphone 6+, this probably has more to do with the form factor than anything else.
I can get about a day and a half out of my S4, but I'm an atypical user since I don't use any messaging aside from E-mail (SMS is stupid and I hope it dies soon).
It's somewhat silly to try to define "using a smartphone as a smartphone" since that's really the ultimate movable goalpost. I use mine primarily to read things on the web while I'm away from a bigger computer and I listen to locally-stored music. I don't really launch other apps, maintain social connections, play games, make calls or look at pornography while on the toilet, all of which might be part of someone else's definition of justifiable smartphone-ing.