Call of Pripyat, on the other hand, has an extremely boring and predictable story (and the story in the original game did a lot for the game's sense of mystery), and the three major areas the player travels through feel kind of like carnivals - there are these "attractions" or "hotspots" where one can find clusters of anomalies, enemy hideouts and such, while the rest of the zone is overall quite empty. This makes travelling from one "attraction" to another quite boring, and making the gameworld feel more constructed and arcade-like.
On the other hand, it is much more stable than the original game, with very little in the way of bugs and glitches, and nearly no gamebreaking ones. One can easily play the vanilla game, no mods, and not have to worry about crashes and the like (although I'd recommend a fov fix as the default fov is at like 65 or something equally horrid). It has many gameplay features not found in the original, such as making looking for artifacts harder and more worthwhile (in SoC they are just scattered across the ground), stashes being properly hidden, sidequests that span over time and maps, as well as being able to repair and upgrade equipment - this last one probably contributes to the game feeling less unforgiving, but it also makes it a bit easier, again making the gameworld feel less oppressive.
Now you may think I hate CoP, but I actually don't, I think it's a great game, both on its own and as a Stalker game - it's just when comparing it to the original game I have to favor the original, as the atmosphere and overall impression of that game had a much bigger impact on me, and CoP felt more predictable. Both are well worth playing though. I think the perfect Stalker game would combine the best parts of SoC and CoP, too bad we won't ever see Stalker 2.
For second playthroughs of the games, I recommend
http://www.moddb.com/mods/old-good-stalker-evolution
for Shadow of Chernobyl, and
Sigerous Mod 1.7 for Call of Pripyat. Both of these keep much of the atmosphere and overall feel of the vanilla games intact while adding stuff like more missions, weapons, items, and characters, without adding a lot of unnecessary shit like so many other mods do - I believe later versions of Sigerous Mod also do this, which is why I recommend 1.7.
Regarding OGSE, the only thing I didn't like was that the ambient music is disabled, which kinda ruins the atmosphere. This is supposedly easily fixed by messing with some config file, but I have no idea how as googling didn't help me get much wiser.
Clear Sky can easily be skipped.