Simply both are smooth, but Z1 is lot more reliable for very long run. Z1 can give same service that you get when it is new for up-to 2years+(even if you throw any thing you throw on it and push it to its max limits even without external memory it runs like a gem) where as Samsung can only give for 1year(hardly, only if you use it without throwing a lot pressure on it then it would last a bit longer).
But Note 3 is no match for Z1 in battery. Give you a example. My experience with it- I had hardly 20% battery in the morning while stepping out for at 7am college. I used the phone for browsing in college and for sharing files using shareit and superbeam. As I travel in metro I always listen to music in the train. The travel time is 1.45hr-2hr. I called my parent 3-4 times and every time the call was nearly 15-20min long. The only thing I dint do is play games on that day as my battery was very low. At the end when I reached home at 5pm I still had 4% battery left. For sure Note 3 cannot do that.