Take the comments with a grain of salt. Passions run high and their are fan boys and girls on both sides of the spectrum. I can't stress enough that both are great phones and sometimes it's the things that the reviews don't mention that can mean a great deal to a particular user.
For example, the One has an LED status light BUT it only blinks 2 colors, green and amber. By contrast, the S3/S4 allows you to tweak the LED to a variety of colors. I use my status light so I can differentiate among notifications. Red is a text from my wife, quick flashing light blue is work email, green is a facebook message etc. By doing this, I dont have to turn on the screen to know what notifications are waiting for me and thereby I save battery life.
Again, with the One, you can only turn on the phone by using the power button which is located awkwardly for right handers and is flush with the phone. The S3/S4 lets you wake the phone with the home button too, making it much easier.
Reviews rarely mention things like this.
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Great sig!