So I have owned one for a month now, I upgraded from a 3 year old iPhone 4, so this is my first foray into Android, here are my impressions.
Positives
USB 3 charger charges so DAMN FAST, I love it, when its dying, I just put it
LOVE LOVE LOVE the multi colored LED in the phone, using MultiFlow its nice to change the color of the led depending on the app that got the notification, if my LED is blinking white I know its a text message, if its purple, its Viber, awesome.
Negatives
Once very week my phone's physical buttons stop working, HOme button doesnt work, if I hold the power button it doesnt bring out the power menu, eventually the phone will restart itself??? Again, I might have too many widgets and apps installed but I thought I would never see something like that in a device with 3GB of Ram.
Other Android chargers have a really difficult time charging the Note 3, as a matter of fact, I cant charge mine with a computer or a car adapter, a USB 2 wall adapter charges it but very very slowly.
The phone will last me more than a day only if I dont use the screen, if I start browing reddit, GAF or anything else, the battery starts draining really really fast not lasting even a day, this is using the AUTO brightness settings.
Phone gets really hot when Dropbox starts uploading all my pictures in the background and it will drain my battery until It cant anymore, I wish I could tell dropbox to only sync while the phone is charging or something.
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I have tons of more positives that have more to do with Android than the Note itself, all in all im very happy with this phone, I bought a knockoff 4200mAh battery so hopefully I see more battery life out of it.