I've owned both (currently the s5) and battery life on the note 3 will be a bit better (not a lot better, just a little) but the trade off is the note is a VERY LARGE phone and while its easy to see that off hand, its another to live with it...it proved to be too big for me.
While I don't have a GS5, I do have a Note 3. Before I bought the phone, I feared the size would be barely manageable. But it didn't take much use at all to realize that the device was well inside the range of what I considered easy to use. The screen is gorgeous, and I have found the extra size makes a huge difference, especially when working with text. Making posts to sites like this one are a breeze, while they were very cumbersome and discombobulating on my previous device, the Galaxy S II.
Bottom line. I recommend you try the device for yourself and then make up your mind about the size.