Bought an s5 last week, really nice phone. I loved image quality of the screen on it. However decided to try a note 3 out and I like it more. The s5 imo looks more aesthetically pleasing and the screen looks better to me. However I didn't like the size of the phone. I only realized this after using the note 3. The s5 is a size for me where one handed sucked and two handing still was kind of strange. I wanted a smaller phone for one handed use. Then after having the note 3, I realized I can two hand type really well and comfortably on the note vs the s5 which was uncomfortable both one or two handed for me. It's weird. Anyway I think both are nice phones however the main thing that pushed me over was having root and roms. The bloatware pissed me off and even the note 3 had a ton of **** and popups before I could root it. Luckily I found someone selling still on 4.3.
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Galaxy Note 3 AT&T on Dynamic Kat 3.0