AMK Mod
Oblivion-Lost
Priboi Story
ABC Inferno
These four are the "biggest" ones. The next ABC Inferno, namely version 1.2, is pretty much the biggest in terms of changes and new content, but that version isn't released even though it's officially completed, according to the last messages from the author, russo, on the Oblivion-Lost.de's discussion forums. He (russo) hasn't been on since a while and we're all wondering what's going on, but the last time he talked about it he mentioned that it was technically completed, but he has a very slow Internet connection, and he needs to upload it from another location since he can't do it from home.
Meanwhile, the others I mentioned, or even the current ABC Inferno version (1.1) are all great mods. I myself am using AMK Mod right now, it's like a toned down version of Clear Sky in certain situations and thanks to certain features, such as NPC's throwing grenades or dragging corpses around, and some more. I've never tried Priboi Story but I heard it's great, you take on the role of a Military and you play the game from their point of view, you start somewhere else, with different weapons, and the situation in the Zone is relatively different too. The Oblivion-Lost mod is a much closer feel to the original ideas that GSC had for Shadow of Chernobyl, and the latest version adopted the dynamic anomalies system that we could (and still can) find in AMK Mod prior to it. The blowouts in AMK are random but the NPC's communication system of the mod allows the NPC's to speak about it a few hours before it occurs.
There's many great mods for Shadow of Chernobyl, and as I said in my humble opinion the best ones are both AMK Mod and Oblivion-Lost, those two are equal in my book, in fact I play both and I alternate between them as I see fit. I can't wait for ABC Inferno 1.2 however, and when it's released I will certainly spend most of my time on it instead of Clear Sky or any other games for that matter, I do feel like playing through Shadow of Chernobyl again but I need something new this time. By the way Oblivion-Lost is quite less randomized than AMK Mod, in O-L you pretty much follow the story and scripted events with some random encounters thrown in but it's nothing that different when compared to vanilla, but in AMK Mod you'll see many more mutants and they'll often be roaming around more freely than in O-L or vanilla SOC, but the story still works of course, but the risks of seeing broken quests are certainly present, even though I've only seen it happen once so far.