I just got my Verizon Wireless Galaxy S4 yesterday.
While my time with it has been brief, I have been very impressed with the device overall.
First, the screen is GORGEOUS!!! I thought my wife's Note 2 had an awesome screen. The new AMOLED display on the S4 is in a league all on it's own, though. Text is just awe-inspiring. Video is absolutely beautiful. The colors are rich, vibrant, and pop. It's not over-saturated like AMOLED screens of old. The color is actually believable and beautiful...It is stunning!
Second, this phone is so powerful compared to my old Droid X2. All games that I've played so far have played perfectly and without stutter. On all benchmarks, this device is at the top of it's class. Browsermark says it's faster than 98% of other smartphones out there... and amazingly, when running the desktop version, it says it's faster than 13% of desktops. I got a chuckle out of that.
I've tried slowing this phone down, and I simply cannot. It is snappy about 95% of the time, and for me, that's perfect.
Third, this phone is very light... crazy light. The otterbox I put on it took care of that issue.
Fourth, from what I can tell, battery life is very good. I can flog this thing hard, and it will easily outlast my old Droid X2 on battery life. Unfortunately, my wife's Note 2 is still the king when it comes to battery life.
Lots of useless gimmicks. I tried using them, and it's apparent that the stuff that uses your eyes and gestures for motion still need some work (or I'm just doing it wrong)
The plastic does look cheap when compared to metal phones. However, since it's in an Otterbox, it doesn't really bother me.
There is a learning curve, but I'm getting used to it very quickly.
Overall, the S4 is a stellar phone. I like it better than the HTC One, but I will concede that both phones are amazing. Choose one and be happy. I'm definitely happy with my S4.