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.