You know its not really bigger than the lumia 920, right? Just smaller bezels?
As for smoothness, this is from anandtech:
"UI performance is finally at the point on most of these modern devices where it’s just amazingly smooth throughout everything. The Galaxy S 4 is no exception here."
So... Yeah, dat lag.
Edit: i watched the video again from anandtechs hands on, and i see that it doesn't react as fast as it should on certain things, like his hover-gestures and in the gallery. This hasn't been the case on any of the other videos ive seen, perhaps an earlier version or a really bogged down device? But from that video alone i can see that a sceptic would interpret that as a laggy device.
However, as you can see above, in their written reviews they maintain its smoothness, and combined with the fact that no lag was evident in any of the other videos ive seen, it doesn't support the notion that the s4 is laggy.
Last time , many websites said Note 2 is smooth and here is experience in real world
Take Note 2 , S3 etc. Any device with 4.x made by Samsung's touchwiz skin.
Press home button and it takes atleast 0.5 seconds to react and try same with iPhone or WP , Reaction is like reflex action.
Definitely there is lot of lag.
My dad has a Note 2 and everytime It lags , Definitely u can notice it.
For example : My lumia has 6000+ photos and I can immediately see those photos (Opening up gallery or selecting a photo , everything is instant even iPhone gets smoked in this respect , only lag from WP is music player) while on Note 2 there are 5,500 photos and it has it takes minimum 2 seconds to open those list of photos and another 0.5 second to load up the first photo.
Tried same with Galaxy S2 running 2.3 , its very fast compared to Note 2 or S3.
It has something to do with touchwiz or 4.x , 2.3 was great with no issues and no matter what device i saw till now in shop or home , All galaxy devices with 4.x irrespective of specs always lagged.They perform somewhat like my iPod 4th gen running iOS 6.
Device is fast but navigation and small things are horribly lagged.For example , loading contacts or opening up music player with huge library , S2 is still fast than note 2 or S3.
I think it has to do with touchwiz , so much crap samsung has added to android.
P.S : I wanted to get Note 2 till last minute and I was afraid of horrible lags after seeing my dad's and got an 820 finally.