A few words:
Screen - simply amazing and by far the best feature of the phone. This is my first AMOLED phone (coming from a Xperia S using a LCD screen) but I have used a few GS3s before, the best screen I have come across (yet to fully play with a HO). The colours are very rich and everything jumps out at you, websites looks very crisp - not really tried any videos other than one supplied but it also looked great. Shortly after getting the phone I went into town and it was quite a sunny afternoon, it held up fairly well but there were a couple of occasions when the sun made it a little difficult to see, turning up the brightness helped but only a little.
Look & Feel - most of this probably comes down to personal choice but whilst I appreciate the HO and XZ are more premium looking phones - this isn't exactly an ugly duckling. I was quite critical of the GS3 when announced for its looks but it grew on me over time. Personally I think the GS4 looks rather stylish considering it's plastic, definitely more premium than the GS3. I was surprised by the weight - it's quite light but not so light it feels like it's going to fly off out your hand. Using one handed is fine - the buttons all feel right though I am coming from a phone with completely different button placement. The up volume rocker is a tad more difficult for me to use and I initially found myself accidentally pressing a key on the bottom right keyboard instead of the back key a few times. I do miss a dedicated camera key though. Lastly it feels comfortable in the hand and doesn't slip easily.
Battery - another impressive feature. I got the phone with around 55% charge and over the next seven hours used the phone quite heavily with a screen on time of almost 3 hours. I did do a very quick charge part way when I swung by my office. Got home with around 5% left. To put into contrast; my Xperia S has been off charge for 2hrs 41mins with 43mins screen time and lost a quarter of its charge. Doing what I did last night with the GS4 on 100% would have almost drained it. Reckon I should be able to get a full day or more with moderate-heavy(ish) usage.
Performance - this is an area that is a little bit patchy. The phone runs fine, loving Project Butter, and handles anything you throw at it with ease (got a shade under 25,000 in AnTuTu). However I have noticed several times a skip/bump when switching between apps or going back to the home screen. Hopefully this can be fixed with an update.
Camera - I haven't really the chance to play with the camera much but for the brief time I have - I was very impressed with the results. Coming from my '12MP' Xperia S - it's like night and day! Pictures look very sharp for a phone and the camera offers you a whole bunch of options. I took a couple below - excuse my friend's pose (he's an Apple fan boy
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Normal mode
Beauty mode
As you can see it has smoothened parts of his face including his nose.
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Summary - I have barely scratched the surface but so far this phone has matched/exceeded my expectations. A worthy upgrade from my XS - possibly not so much from the GS3. Other than the slight performance bug there is very little I fault with this phone.
. Only had a quick play, but coming from an iPhone 4S the plastic feeling is no where near as bad as I thought it'd be. I actually think the black mist version looks quite nice 
